Question
Q1 The number of bacteria triples every 5 days. If the bacteria population starts with 10 bacteria, then the equation A(t) = 10(3)^0.2t can represent the number of bacteria. Find the value for A(15).
Answers
GPT-4o mini
To find the value of \( A(15) \) using the equation \( A(t) = 10(3)^{0.2t} \), we simply need to substitute \( t = 15 \) into the equation.
\[
A(15) = 10(3)^{0.2 \times 15}
\]
Calculating \( 0.2 \times 15 \):
\[
0.2 \times 15 = 3
\]
Now we can substitute this value back into the equation:
\[
A(15) = 10(3)^{3}
\]
Next, we calculate \( 3^3 \):
\[
3^3 = 27
\]
Now substitute this value back into the equation:
\[
A(15) = 10 \times 27 = 270
\]
Thus, the value for \( A(15) \) is:
\[
\boxed{270}
\]
\[
A(15) = 10(3)^{0.2 \times 15}
\]
Calculating \( 0.2 \times 15 \):
\[
0.2 \times 15 = 3
\]
Now we can substitute this value back into the equation:
\[
A(15) = 10(3)^{3}
\]
Next, we calculate \( 3^3 \):
\[
3^3 = 27
\]
Now substitute this value back into the equation:
\[
A(15) = 10 \times 27 = 270
\]
Thus, the value for \( A(15) \) is:
\[
\boxed{270}
\]