Investment Problems An investment of P dollars is deposited in a savings account that is compounded monthly with an annual interest rate of r , where r is expressed as a decimal. The amount of money A in the account after t years is given by A = P ( 1 + r / 12 ) 12 t . Use this equation to complete the following exercises. 63. Determine the time it takes an investment of $1000 to increase to $1100 dollars if it is placed in an account that is compounded monthly with an annual interest rate of 1%( r = 0.01).
Investment Problems An investment of P dollars is deposited in a savings account that is compounded monthly with an annual interest rate of r , where r is expressed as a decimal. The amount of money A in the account after t years is given by A = P ( 1 + r / 12 ) 12 t . Use this equation to complete the following exercises. 63. Determine the time it takes an investment of $1000 to increase to $1100 dollars if it is placed in an account that is compounded monthly with an annual interest rate of 1%( r = 0.01).
Solution Summary: The author explains how the time taken to increase the investment of 1000 to 1100 is 9.53 years.
Investment Problems An investment of P dollars is deposited in a savings account that is compounded monthly with an annual interest rate of r, where r is expressed as a decimal. The amount of money A in the account after t years is given by
A
=
P
(
1
+
r
/
12
)
12
t
. Use this equation to complete the following exercises.
63. Determine the time it takes an investment of $1000 to increase to $1100 dollars if it is placed in an account that is compounded monthly with an annual interest rate of 1%(r = 0.01).
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
Chapter 1 Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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