Natural and human-made substances break down over time and figuring out how much is left over time is very common. The function A(t)=135(.917)t

Question

represents the amount of substance, A(t)
, given the number of days, t
. How much of the substance will be left after 18 days, to the nearest whole value? Find A(18)
.(1 point)

Answer 1

To find the amount of substance left after 18 days using the function \( A(t) = 135(0.917)^t \), we can substitute \( t = 18 \) into the equation:

\[ A(18) = 135(0.917)^{18} \]

First, calculate \( (0.917)^{18} \):

\[ (0.917)^{18} \approx 0.2868 \quad \text{(using a calculator)} \]

Now multiply this value by 135:

\[ A(18) = 135 \times 0.2868 \approx 38.6 \]

Rounding to the nearest whole value:

\[ A(18) \approx 39 \]

Thus, the amount of substance left after 18 days is approximately 39.