Question

jia li found a collection of baseball cards worth $8,000 in her attic. it is estimated to increase in value by 15% per year. write a function and find the value of the collection after 7 years
a function that represents this situation is f(x) =
(type an expression using x as the variable. simplify your answer. use integers or decimals for any numbers in the expression. do not include the $ symbol in your answer.)

Explanation:

Step1: Identify growth formula type

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

Step2: Plug in given values

Initial value $P=8000$, growth rate $r=0.15$.
$f(x) = 8000(1+0.15)^x = 8000(1.15)^x$

Step3: Calculate value at x=7

Substitute $x=7$ into the function.
$f(7) = 8000(1.15)^7$
First compute $1.15^7 \approx 2.66002$
Then $8000 \times 2.66002 = 21280.16$

Answer:

A function that represents this situation is $f(x)=8000(1.15)^x$
The value of the collection after 7 years is $\$21280.16$