Question

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.

Answer 1

Answer:

Part 1) $y=7.50(1.06)^x$

Part 2) $\ 38.34$

Step-by-step explanation:

Part 1) Write an exponential growth function

we know that

The equation of a exponential growth function is given by

$y=a(1+r)^x$

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

$a=\ 7.50\\r=6\%=6/100=0.06$

substitute

$y=7.50(1+0.06)^x$

$y=7.50(1.06)^x$

Part 2) Find the baseball cards value in 2015.

Find the value of x

$x=2015-1987=28\ years$

substitute the value of x in the equation

$y=7.50(1.06)^{28}=\ 38.34$