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

Answer 1

The multiplicative rate of change that should be in Hal’s function = 49/50=0.98

=9.8×10⁻¹

Step-by-step 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.

Hope his helps! ;)