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

It will be $10,000 that is >decreasing< at a rate of 2% per year, we therefore assume compound interest.

That will be:
$10,000 x (1.0-2%)^#of years
which is
£10,000 x (1.0-0.02)^#ofyears
£10,000 x (0.98)^#ofyears

This is because if we multiply it by 1 to the power of the number of years, you end up with the same number. In order to decrease it, we need to multiply it by a factor which will make its value smaller.

The multiplicative rate of change here would be: 0.98

Answer 2

To demonstrate:

1st year: $10,000 x 0.98 = 9800
Take 9,800 as the base for the second year
9,800 x 0.98 = $9,604
Take 9,604 as the base for the next year
" = $9411.92

This shows that the $ he will have is decreasing
Sad times