Question

1. 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.

Explanation:

Step1: Identify decay factor

The function is $A(t)=145(0.95)^t$, which follows the exponential decay/growth form $A(t)=a(1+r)^t$, where $1+r$ is the growth/decay factor. Here, the factor is $0.95$.

Step2: Calculate rate of change

Subtract the decay factor from 1 to find the rate: $1 - 0.95 = 0.05 = 5\%$. Since $0.95<1$, this is a decrease.

Answer:

The rate of change in the value of the guitar is modeled by $\boldsymbol{0.95}$, which represents $\boldsymbol{a\ decrease\ of}$ $\boldsymbol{5\%}$ per year.