Question

Cindy found a collection of baseball cards in her attic worth $8,000. the collection 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

Answer 1

An exponential growth function for Cindy's baseball card collection is A(t) = 8000(1 + 0.015)^t. After 7 years, the value of the collection is approximately $8,913.09.

Step-by-step explanation:

To write an exponential growth function for Cindy's collection of baseball cards, we can apply the formula for exponential growth:

A(t) = P(1 + r)^t

Where:

• A(t) is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• t is the time the money is invested for, in years.

In Cindy's case, P is $8,000, r is 1.5% or 0.015, and t will be the number of years we are calculating the growth for. The exponential growth function for Cindy's baseball card collection becomes:

A(t) = 8000(1 + 0.015)^t

To find the value of the collection after 7 years, we substitute 7 for t:

A(7) = 8000(1 + 0.015)^7

By calculating A(7), we find that the collection will be worth approximately:

A(7) ≈ $8,913.09

Answer 2

a]
Exponential function is given by the form:
y=a(b)ˣ
where:
a=initial value
b=growth factor
From the question:
a=$8000, b=1.015,
thus the exponential growth function of this situation is:
y=8000(1.015)ˣ

b] The value of the collection after 7 years will be:
x=7 years
Using the formula:
y=8000(1.015)ˣ
plugging the values we get:
y=8000(1.015)⁷
y=8,878.76

Answer: $8,878.76