Question

cindy found a collection of baseball cards in her attic worth $8,000. it is estimated to increase in value by 1.5% per year. write an exponential growth function and find the value of the collection after 7 years.

the exponential growth function that represents this situation is f(x) =
(simplify your answer.)

Explanation:

Step1: Recall growth function form

The standard exponential growth function is $f(x) = P(1+r)^x$, where $P$ is initial value, $r$ is growth rate, $x$ is time.

Step2: Identify given values

$P = 8000$, $r = 0.015$ (1.5% converted to decimal)

Step3: Write the growth function

Substitute values: $f(x) = 8000(1+0.015)^x = 8000(1.015)^x$

Step4: Calculate value at $x=7$

Substitute $x=7$: $f(7) = 8000(1.015)^7$
Calculate $(1.015)^7 \approx 1.109845$
Then $8000 \times 1.109845 \approx 8878.76$

Answer:

Exponential growth function: $f(x) = 8000(1.015)^x$

Value after 7 years: $\$8878.76$