Question
The population of fish in a lake is initially 300 and increases by 1.5% each year thereafter. What will be the population of the fish after 7 years?
A.
269
B.
5125
C.
5
D.
332
A.
269
B.
5125
C.
5
D.
332
Answers
GPT-4o mini
To calculate the population of fish in the lake after 7 years, given that it starts at 300 and increases by 1.5% each year, we can use the formula for exponential growth:
\[
P(t) = P_0 \times (1 + r)^t
\]
where:
- \( P(t) \) is the population after \( t \) years,
- \( P_0 \) is the initial population,
- \( r \) is the rate of growth (as a decimal),
- \( t \) is the number of years.
In this case:
- \( P_0 = 300 \)
- \( r = 1.5\% = 0.015 \)
- \( t = 7 \)
Now we can plug in these values:
\[
P(7) = 300 \times (1 + 0.015)^7
\]
Calculating \( (1 + 0.015)^7 \):
\[
(1.015)^7 \approx 1.1107
\]
Now substitute this back into the equation:
\[
P(7) = 300 \times 1.1107 \approx 333.21
\]
Since population must be a whole number, we round it to 333. Thus, the population of fish after 7 years is approximately 333.
None of the given options (A. 269, B. 5125, C. 5, D. 332) matches exactly. However, the closest answer is:
**D. 332**.
\[
P(t) = P_0 \times (1 + r)^t
\]
where:
- \( P(t) \) is the population after \( t \) years,
- \( P_0 \) is the initial population,
- \( r \) is the rate of growth (as a decimal),
- \( t \) is the number of years.
In this case:
- \( P_0 = 300 \)
- \( r = 1.5\% = 0.015 \)
- \( t = 7 \)
Now we can plug in these values:
\[
P(7) = 300 \times (1 + 0.015)^7
\]
Calculating \( (1 + 0.015)^7 \):
\[
(1.015)^7 \approx 1.1107
\]
Now substitute this back into the equation:
\[
P(7) = 300 \times 1.1107 \approx 333.21
\]
Since population must be a whole number, we round it to 333. Thus, the population of fish after 7 years is approximately 333.
None of the given options (A. 269, B. 5125, C. 5, D. 332) matches exactly. However, the closest answer is:
**D. 332**.