Question
A chemical compound decomposes by 3% each day. The function C(t)=1500(0.97)t represents the amount of compound remaining after t days. How much of the compound remains after 12 days? Find C(12).
Answers
GPT-4o mini
To find the amount of the compound remaining after 12 days using the function \( C(t) = 1500(0.97)^t \), we can substitute \( t = 12 \) into the equation.
\[
C(12) = 1500(0.97)^{12}
\]
First, we need to calculate \( (0.97)^{12} \):
\[
(0.97)^{12} \approx 0.6860 \quad \text{(using a calculator)}
\]
Now we can multiply this value by 1500:
\[
C(12) \approx 1500 \times 0.6860 \approx 1029.00
\]
Therefore, the amount of the compound remaining after 12 days is approximately:
\[
\boxed{1029}
\]
\[
C(12) = 1500(0.97)^{12}
\]
First, we need to calculate \( (0.97)^{12} \):
\[
(0.97)^{12} \approx 0.6860 \quad \text{(using a calculator)}
\]
Now we can multiply this value by 1500:
\[
C(12) \approx 1500 \times 0.6860 \approx 1029.00
\]
Therefore, the amount of the compound remaining after 12 days is approximately:
\[
\boxed{1029}
\]