College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter6: Exponential And Logarithmic Functions
6.1 Exponential Functions 6.2 Graphs Of Exponential Functions 6.3 Logarithmic Functions 6.4 Graphs Of Logarithmic Functions 6.5 Logarithmic Properties 6.6 Exponential And Logarithmic Equations 6.7 Exponential And Logarithmic Models 6.8 Fitting Exponential Models To Data Chapter Questions Section6.1: Exponential Functions
Problem 1TI: Which of the following equations represent exponential functions? • f(x)=2x23x+1 • g(x)=0.875x •... Problem 2TI: Let f(x)=8(1.2)x5. Evaluate f(3) using a calculator. Round to four decimal places. Problem 3TI: The population of China was about 1.39 billion in the year 2013, with an annual growth rate of about... Problem 4TI: A wolf population is growing exponentially. In 2011, 129 wolves were counted. By 2013, the... Problem 5TI: Given the two points (1,3) and (2,4.5) , find the equation of the exponential function that passes... Problem 6TI: Find an equation for the exponential function graphed in Figure 6. Problem 7TI: Use a graphing calculator to find the exponential equation that includes the points (3,75.98) and... Problem 8TI: An initial investment of 100,000 at 12 interest is compounded weekly (use 52 weeks in a year). What... Problem 9TI: Refer to Example 9. To the nearest dollar, how much would Lily need to invest if the account is... Problem 10TI: Use a calculator to find e0.5. Round to five decimal places. Problem 11TI: A person invests 100,000 at a nominal 12 interest per year compounded continuously. What will be the... Problem 12TI: Using the data in Example 12, how much radon-222 will remain after one year? Problem 1SE: Explain why the values of an increasing exponentialfunction will eventually overtake the valuesof... Problem 2SE: Given a formula for an exponential function, is itpossible to determine whether the function grows... Problem 3SE: The Oxford Dictionary defines the word nominal asa value that is “stated or expressed but... Problem 4SE: For the following exercises, identify whether the statement represents an exponential function.... Problem 5SE: For the following exercises, identify whether the statement represents an exponential function.... Problem 6SE: For the following exercises, identify whether the statement represents an exponential function.... Problem 7SE: For the following exercises, identify whether the statement represents an exponential function.... Problem 8SE: For the following exercises, identify whether the statement represents an exponential function.... Problem 9SE: For the following exercises, consider this scenario: For each year t, the population of a forest... Problem 10SE: For the following exercises, consider this scenario: For each year t , the population of a forest of... Problem 11SE: For the following exercises, consider this scenario: For each year t , the population of a forest of... Problem 12SE: For the following exercises, consider this scenario: For each year t , the population of a forest of... Problem 13SE: For the following exercises, consider this scenario: For each year t , the population of a forest of... Problem 14SE: For the following exercises, determine whether the equation represents exponential growth,... Problem 15SE: For the following exercises, determine whether the equation represents exponential growth,... Problem 16SE: For the following exercises, determine whether the equation represents exponential growth,... Problem 17SE: For the following exercises, determine whether the equation represents exponential growth,... Problem 18SE: For the following exercises, find the formula for an exponential function that passes through the... Problem 19SE: For the following exercises, find the formula for an exponential function that passes through the... Problem 20SE: For the following exercises, find the formula for an exponential function that passes through the... Problem 21SE: For the following exercises, find the formula for an exponential function that passes through the... Problem 22SE: For the following exercises, find the formula for an exponential function that passes through the... Problem 23SE: For the following exercises, determine whether the table could represent a function that is linear,... Problem 24SE: For the following exercises, determine whether the table could represent a function that is linear,... Problem 25SE: For the following exercises, determine whether the table could represent a function that is linear,... Problem 26SE: For the following exercises, determine whether the table could represent a function that is linear,... Problem 27SE: For the following exercises, determine whether the table could represent a function that is linear,... Problem 28SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. After a certain... Problem 29SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. What was the initial... Problem 30SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. How many years had... Problem 31SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. An account is opened... Problem 32SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. How much more would... Problem 33SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. Solve the compound... Problem 34SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. 34. Use the formula... Problem 35SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. 35. How much more... Problem 36SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. Use properties of... Problem 37SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. Use the formula... Problem 38SE: For the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. Use the formula... Problem 39SE: For the following exercises, determine whether the equation represents continuous growth, continuous... Problem 40SE: For the following exercises, determine whether the equation represents continuous growth, continuous... Problem 41SE: For the following exercises, determine whether the equation represents continuous growth, continuous... Problem 42SE: For the following exercises, determine whether the equation represents continuous growth, continuous... Problem 43SE: For the following exercises, determine whether the equation represents continuous growth, continuous... Problem 44SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 45SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 46SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 47SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 48SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 49SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 50SE: For the following exercises, evaluate each function. Round answers to four decimal places, if... Problem 51SE: For the following exercises, use a graphing calculator to find the equation of an exponential... Problem 52SE: For the following exercises, use a graphing calculator to find the equation of an exponential... Problem 53SE: For the following exercises, use a graphing calculator to find the equation of an exponential... Problem 54SE: For the following exercises, use a graphing calculator to find the equation of an exponential... Problem 55SE: For the following exercises, use a graphing calculator to find the equation of an exponential... Problem 56SE: The annual percentage yield (APY) of an investmentaccount is a representation ofthe actual interest... Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily.... Problem 58SE: Recall that an exponential function is any equationwritten in the form f(x)=abx such that a and b... Problem 59SE: In an exponential decay function, the base of theexponent is a value between 0 and 1. Thus, for... Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is... Problem 61SE: The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012,... Problem 62SE: A scientist begins with 100 milligrams of aradioactive substance that decays exponentially. After 35... Problem 63SE: In the year 1985, a house was valued at 110,000. Bythe year 2005, the value hadappreciated to... Problem 64SE: A car was valued at 38,000 in the year 2007. By 2013, the value had depreciated to 11,000 If the... Problem 65SE: Jamal wants to save 54,000 for a down paymenton a home. How much will he need to invest in anaccount... Problem 66SE: Kyoko has 10,000 that she wants to invest. Her bankhas several investment accounts tochoose from,... Problem 67SE: Alyssa opened a retirement account with 7.25 APRin the year 2000. Her initial deposit was 13,500.... Problem 68SE: An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000... Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Easy differential equations problem, I will rate and like . Thank you!
Transcribed Image Text: 2. See the following problem:
Justify all solutions (give English explanations as you answer)
y' = 3y²/3
y(0) = 0.
a. Show that the constant function, y(t) = 0, is a solution to the initial value
problem.
b. Show that
y(t)
=
0,
t< to
(t-to)³, t> to
is a solution for the initial value problem, where to is any real number.
Hence, there exists an infinite number of solutions to the initial value
problem. [Hint: Make sure that the derivative of y(t) exists at t = to. ]
c. Explain why this example does not contradict the Existence and
Uniqueness Theorem.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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Step 1: (a) Show that y=0 is a solution
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Step 2: (b) find solution Analytically
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![2. See the following problem:
Justify all solutions (give English explanations as you answer)
y' = 3y²/3
y(0) = 0.
a. Show that the constant function, y(t) = 0, is a solution to the initial value
problem.
b. Show that
y(t)
=
0,
t< to
(t-to)³, t> to
is a solution for the initial value problem, where to is any real number.
Hence, there exists an infinite number of solutions to the initial value
problem. [Hint: Make sure that the derivative of y(t) exists at t = to. ]
c. Explain why this example does not contradict the Existence and
Uniqueness Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2acb91cb-06a2-4f4a-b63b-95f3aaaf3e2a%2Fbe1f6382-3760-4d7d-9041-ce1ecabef4a6%2Fe94rjss_processed.png&w=3840&q=75)
