Find the exponential function that satisfies the given conditions: initial value = 66, decreasing at a rate of 0.5% per weekf(t) = 0.5 ⋅ 0.34tf(t) = 66 ⋅ 1.5tf(t) = 66 ⋅ 0.995tf(t) = 66 ⋅ 1.005t

f(t) = 66·0.995^t

Step-by-step 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.