Question

hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. what multiplicative rate of change should hal use in his function?
○ 0.02
○ 0.98
○ 1.02
○ 1.98

Explanation:

Step1: Understand the problem

We have an investment decreasing at 2% annually. For exponential decay, the formula for the value \( V(t) \) of an investment with initial value \( P \), rate of decrease \( r \) (in decimal) after \( t \) years is \( V(t)=P(1 - r)^t \). The multiplicative rate of change is the base of the exponential function, which is \( 1 - r \).

Step2: Calculate the multiplicative rate

The rate of decrease \( r = 2\%=0.02 \). So the multiplicative rate of change is \( 1 - 0.02=0.98 \).

Answer:

0.98