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

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)
Responses

29
29 - incorrect

30
30 - no response given

28
28 - no response given

25

1 answer

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

Let's calculate \( A(18) \):

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

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

\[ (0.917)^{18} \approx 0.292 \]

Then, multiply that result by 135:

\[ A(18) \approx 135 \times 0.292 \approx 39.42 \]

Now rounding this to the nearest whole number gives us:

\[ A(18) \approx 39 \]

Since the nearest whole number is not given in your responses, it seems like you may need to verify the calculations or see if there was a misunderstanding with the function. The correct value appears to be around 39, which isn't listed among the provided responses. Please ensure the function or responses are correctly stated.