Question

Brandon purchased a new guitar in 2012. The value of his guitar, t years after he bought it, can be modeled by the function A(t)=145(0.95)t.

Drag and drop the answer to the boxes below to complete the sentence.

145, 0.95
a decrease of, an increase of
5%, 45%, 95%

The rate of change in the value of the guitar is modeled by _____, which represents _____________ ______ per year.

Answer 1

Answer: The rate of change in the value of the guitar is modeled by 0.95, which represents a decrease of 5% per year.

Explanation:

Hi, to answer this question we have to apply an exponential decay function:

A = P (1 - r) t

Where:

p = original price

r = decrease rate (decimal form)

t= years

A = price after t years

Replacing with the values given:

A(t)=145(0.95)t.

Where

0.95 = 1-r

0.95-1 = r

-0.05 =-r

0.05 =r

Converting to percentage form:

0.05 x 100 = 5%

Feel free to ask for more if needed or if you did not understand something.