Question

Write a function in terms of t that represents the situation.

Sales of $10,000 increase by 65% each year.
y =
13

Answer 1

A function in terms of t that represents the situation is:

`\:y\:=\:10,000\left(1.65\right)^t`

Explanation:

We know that the exponential growth function is of the form

`y\:=\:a\:\left(1\:+\:r\right)^t`

Here:

• a = initial value

• r = growth rate

• t = number of time intervals that have passed

As the sales of $10,000 represent an initial condition. Thus,

a = 10,000

Given that sales are increased by 65% every year.

r = 65% = 0.65

now substituting a = 10,000 and r = 0.65 in the function

`y\:=\:10,000\left(1\:+\:0.65\right)^t`

`\:y\:=\:10,000\left(1.65\right)^t`

Therefore, a function in terms of t that represents the situation is:

`\:y\:=\:10,000\left(1.65\right)^t`