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?

Answer 1

Answer: B

Step-by-step explanation:

0.98

E2020

Answer 2

Answer
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98
                                                                                                                   =9.8×10⁻¹

Explanation
The investment of $10,000 decreases by 2% every year. So the following year is usually (100 - 2)=98% of the previous year. This is a geometric progression.
In this case the first term = 10000
The second term = 98% × 10000 = 9800.
The common ratio = 9800/10000=49/50
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98.
The equation of the exponential rate would be;
10,000ₓ0.98ⁿ.
where n is the number years.