Question

Find the exponential function that satisfies the given conditions:

Initial value = 66, decreasing at a rate of 0.5% per week

f(t) = 0.5 ⋅ 0.34t

f(t) = 66 ⋅ 1.5t

f(t) = 66 ⋅ 0.995t

f(t) = 66 ⋅ 1.005t

Answer 1

f(t) = 66·0.995^t

Explanation:

You can try t=0 and t=1 in each of the formulas to see which one gives values of 66 and 0.5% less than 66, or 65.67.

The first function has an initial value of 0.5, so is not correct.

The second function gives f(1) = 99, so is not correct.

The third function gives f(1) = 65.67, so is correct.

The fourth function gives f(1) = 66.33, so is not correct.

_____

You can realize that the multiplier will be 0.5% less than 100%, so will be 99.5% = 0.995. This number shows up only in the third selection.