Write an exponential function for the situation below and use your equation to answer the question.

Question

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A population of 10 rabbits doubles in size every month. How many rabbits will there be after 8 months?

Answer 1

To model the population of rabbits, we can use the exponential growth formula:

\[ P(t) = P_0 \cdot 2^{t} \]

Where:

• \( P(t) \) is the population at time \( t \),
• \( P_0 \) is the initial population,
• \( t \) is the time in months,
• The base 2 indicates that the population doubles.

In this scenario:

• The initial population \( P_0 = 10 \) rabbits,
• The time \( t = 8 \) months.

Substituting the values into the equation:

\[ P(8) = 10 \cdot 2^{8} \]

Now we calculate \( 2^8 \):

\[ 2^8 = 256 \]

Now we can substitute \( 256 \) back into the equation:

\[ P(8) = 10 \cdot 256 \] \[ P(8) = 2560 \]

Thus, after 8 months, the rabbit population will be 2560 rabbits.