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

𝐴
(
𝑡
)
=
135
(
.917
)
𝑡
represents the amount of substance, A(t)
𝐴
(
𝑡
)
, given the number of days, t
𝑡
. How much of the substance will be left after 18 days, to the nearest whole value? Find A(18)
𝐴
(
18
)
.(1 point)
Responses

29
29 - no response given

25
25 - no response given

28
28 - no response given

30

Answer 1

To find out how much of the substance will be left after 18 days using the function \( A(t) = 135(0.917)^t \), we can substitute \( t = 18 \) into the equation.

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

Calculating \( (0.917)^{18} \):

\[ (0.917)^{18} \approx 0.302 \]

Now substitute this value back into the equation:

\[ A(18) \approx 135 \times 0.302 \approx 40.77 \]

Now round it to the nearest whole number:

\[ A(18) \approx 41 \]

However, none of the provided options of 29, 25, 28, or 30 match this result, so please double-check the function or calculations provided. If the original function or parameters change, we can re-evaluate accordingly!