Question

If a baseball card appreciates exponentially in value by 50% over 10 years, what is its annual appreciation (growth) rate? Please use a calculator, and answer to the nearest whole percent. ​

Answer 1

Using an exponential function, it is found that it's annual growth rate is of 4%.

What is an exponential function?

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^t$

In which:

• A(0) is the initial value.

• r is the growth rate, as a decimal.

In this problem, the card appreciates exponentially in value by 50% over 10 years, hence:

A(10) = 1.5A(0).

Thus:

$A(t) = A(0)(1 + r)^t$

$1.5A(0) = A(0)(1 + r)^{10}$

$(1 + r)^{10} = 1.5$

$\sqrt[10]{(1 + r)^{10}} = \sqrt[10]{1.5}$

1 + r = 1.04.

r = 0.04.

0.04 x 100% = 4%.

It's annual growth rate is of 4%.

More can be learned about exponential functions at brainly.com/question/25537936