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).

Answer 1

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:

\[ \boxed{270} \]