In the following exercise you are asked to relate functional notation to practical explanations of what certain functions mean. The function  T(P, r, m)  gives the time required to pay off an installment loan of P dollars if the APR is r as a decimal and we make monthly payments of m dollars. Use functional notation to indicate the time required to pay off a $12,000 automobile loan at an APR of 5% if the monthly payment is $410.

Q: 80 Height (metres) 40 Y 5 10 15 Time (minutes) 20 25 30

A: A graph of the trigonometric function is given, we have to find the equation of the graph.

Q: The function y=e−3x is vertically stretched by a factor of 4, reflected across the y-axis, and then…

A: Given

Q: Convert the formulaf(t)=136e0.25tf(t)=136e0.25t to the form f(t)=abtf(t)=abt. Write your answer…

A:

Q: Describe the slope of the tangent line to the graph of f(x)= e* for the following. a. x→-0 b. x→0…

A:

Q: Convert the formulaf(t) = 193e-0.03t to the form f(t) = abt. Write your answer using function…

A:

Q: Convert the equation f(t) = 176(0.66) to the form f(t) = aet. Write your answer using function…

A:

Q: The average water level in a retention pond is 6.8 ft. During a time of drought, the water level…

A: We will solve the following.

Q: The price of one share of a company's stock S is tied to its annual profits p in millions of dollars…

A: Given:     Price of one share of company S=0.1p-100     Company sells one share of its stock =$1.84

Q: The following equation approximates the value of the U.S. Consumer Price Index (CPI) from December…

A: Given: It is provided that the graph shows the approximate value of the CPI from December 2006…

Q: Suppose that I wish to open a new savings account. The account accrues 5% interest per year…

A: The savings account accrues 5% interest per year compounded monthly and $15 in fees are deducted…

Q: Set up expressions initially with functional notation like P/F,i,n Priscilla purchased an $8,000, 9%…

A: Given that set up expressions initially with functional notation like P/F,i,n Priscilla purchased an…

Q: (a) Give a formula for the city’s population, P, as a function of the number of years, t, since…

A: To give formulae to for the city’s population as a function number of years(t)  since 2015. Hence…

Q: If Daniella opens a mutual fund account with a deposit of 15,000 and it promises to pay an annual…

A: Consider the provided question, Principal amount, P = 15,000 The annual interest rate of r%…

Q: or 2 % hou

A: answer of given question is in step 2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.