Question
A podcast starts with 400
listeners and grows at 7%
annually.
How many listeners will the podcast have after 5
years?
Round to the nearest whole number.
(2 points)
listeners
listeners and grows at 7%
annually.
How many listeners will the podcast have after 5
years?
Round to the nearest whole number.
(2 points)
listeners
Answers
GPT-4o mini
To calculate the number of listeners after 5 years with a growth rate of 7% annually, you can use the formula for compound growth:
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of listeners after time \( t \)
- \( P \) is the initial amount of listeners (400)
- \( r \) is the growth rate (7% or 0.07)
- \( t \) is the number of years (5)
Plugging in the values:
\[
A = 400(1 + 0.07)^5
\]
Calculating the components step by step:
1. Calculate \( 1 + r \):
\[
1 + 0.07 = 1.07
\]
2. Raise it to the power of \( t \):
\[
1.07^5 \approx 1.40255
\]
3. Multiply by the initial number of listeners:
\[
A \approx 400 \times 1.40255 \approx 561.02
\]
Rounding to the nearest whole number, the podcast will have approximately **561 listeners** after 5 years.
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of listeners after time \( t \)
- \( P \) is the initial amount of listeners (400)
- \( r \) is the growth rate (7% or 0.07)
- \( t \) is the number of years (5)
Plugging in the values:
\[
A = 400(1 + 0.07)^5
\]
Calculating the components step by step:
1. Calculate \( 1 + r \):
\[
1 + 0.07 = 1.07
\]
2. Raise it to the power of \( t \):
\[
1.07^5 \approx 1.40255
\]
3. Multiply by the initial number of listeners:
\[
A \approx 400 \times 1.40255 \approx 561.02
\]
Rounding to the nearest whole number, the podcast will have approximately **561 listeners** after 5 years.