hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at…
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
Answer
Explanation:
Step1: Understand the concept of decay factor
For an exponential - decay function of the form $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time. The multiplicative rate of change is $(1 - r)$.
Step2: Convert the percentage to a decimal
The rate of decrease is $2%$. To convert it to a decimal, we divide by 100, so $r=0.02$.
Step3: Calculate the multiplicative rate of change
Substitute $r = 0.02$ into $(1 - r)$. We get $1-0.02=0.98$.
Answer:
0.98