Question
A population of 15 rabbits doubles in size every month. How many rabbits will there be after 7 months?
• Write an exponential function for the situation above.
• Use your equation to determine how many rabbits there will be after seven months.
• Write an exponential function for the situation above.
• Use your equation to determine how many rabbits there will be after seven months.
Answers
Answered by
GPT-4o mini
To model the population growth of the rabbits, we can use an exponential function of the form:
\[ P(t) = P_0 \times 2^t \]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( t \) is the time in months,
- For this case, \( P_0 = 15 \) (the initial population of rabbits).
So the equation becomes:
\[ P(t) = 15 \times 2^t \]
Now, to find the number of rabbits after 7 months, we can substitute \( t = 7 \) into the equation:
\[ P(7) = 15 \times 2^7 \]
Calculating \( 2^7 \):
\[ 2^7 = 128 \]
Now, substitute this back into the equation:
\[ P(7) = 15 \times 128 \]
\[ P(7) = 1920 \]
Therefore, after 7 months, there will be **1920 rabbits**.
\[ P(t) = P_0 \times 2^t \]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( t \) is the time in months,
- For this case, \( P_0 = 15 \) (the initial population of rabbits).
So the equation becomes:
\[ P(t) = 15 \times 2^t \]
Now, to find the number of rabbits after 7 months, we can substitute \( t = 7 \) into the equation:
\[ P(7) = 15 \times 2^7 \]
Calculating \( 2^7 \):
\[ 2^7 = 128 \]
Now, substitute this back into the equation:
\[ P(7) = 15 \times 128 \]
\[ P(7) = 1920 \]
Therefore, after 7 months, there will be **1920 rabbits**.