Roberta invested $600 into a mutual fund that paid 4% interest each year compounded annually. Write an exponential function of the form y=a (b) x to describe the value of the mutual fund then use that function to determine the value of the mutual fund in 15 years

The exponential equation is A = 600 (1.04) ^15

The value of the mutual fund after 15 years is $1,081

Step-by-step explanation:

The value of the mutual fund after the number of years can be represented using the compound interest equation below;

A = P (1 + r/n) ^nt

Where A is the value of the mutual fund after 15 years, P is the initial amount invested which is $600, r is the interest rate which is 4% or 0.04 (4% = 4/100 = 0.04), n is the number of times we are compounding per year (which is 1 since it is a one time payment per year) and t is the number of years which is 15

Let's plug these values, we have;

A = 600 (1 + 0.04/1) ^15

A = 600 (1.04) ^15

A = $1,081 approximately

y = 600 * (1.04) ^t

for t = 15: y = $1080.57

Step-by-step explanation:

The exponencial function y = a (b) x have the following variables:

a: inicial value

b: rate of interest plus one

x: time invested

So, if the inicial value invested is 600, the rate is 4% and the time is 15 years, we have that the equation is:

y = 600 * (1+0.04) ^t = 600 * (1.04) ^t

And for time t = 15 years, we have that:

y = 600 * (1.04) ^15 = $1080.57