Aaron owns a basketball card. He bought the card for $7.50 in 1987 and it’s value increases by 6% each year. Write and use an exponential growth function to find the baseball cards value in 2015.

The exponential growth is given by the growth rate of subsequent period

raised to power of time.

The given parameter are;

The amount Aaron buys the basketball card in 1987, a = $7.50

The rate at which the value increases each year, r = 6%

To write the exponential growth function.

A general form of the exponential growth function is;

Where;

a = The starting amount = $7.50

r = The growth rate = 6% = 0.06

t = The time duration of the growth = 2015 - 1987 = 28

The time duration, t = 28 years

The exponential growth function to find the basketball card's value in 2015 is therefore;

Which gives;

f(28) = 7.5 × (1 + 0.06)²⁸ ≈ 38.34

Learn more about the exponential growth function here:

link

Part 1)

Part 2)

Step-by-step explanation:

Part 1) Write an exponential growth function

we know that

The equation of a exponential growth function is given by

where

y is the baseballs card value

x is the number of years since 1987

a is the initial value

r is the rate of change

we have

substitute

Part 2) Find the baseball cards value in 2015.

Find the value of x

substitute the value of x in the equation

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: