Question

In 2007, a principal of $4700 was invested at 5.25% Interest, compounded annually.

Let t be the number of years since 2007. Let y be the value of the investment, in dollars.
Write an exponential function showing the relationship between y and t.

Answer 1

The formula for calculating the future value of an investment compounded annually is:

FV = P(1 + r)^t

where:

FV = future value of the investment

P = principal or initial investment

r = annual interest rate as a decimal

t = number of years the investment is held

In this problem, the principal is given as $4700, the annual interest rate is given as 5.25%, and the time is measured in years since 2007.

So we can write the function as:

y = 4700(1 + 0.0525)^t

In this function, y represents the future value of the investment (in dollars) and t represents the number of years since 2007.

The above function can be written in the form A or A B , where A and B are constants or variable expressions that have no variables in common.

A = 4700

B = 1 + 0.0525

y = A*B^t

So the exponential function for the problem is:

y = 4700*(1+0.0525)^t