Question
An amusement park currently has 350
visitors upon opening. Each hour, the number of visitors increases at a rate of 1.2%
due to a special coupon.
To the nearest whole number, predict how many visitors the amusement park will have after 3 hours of being open.
__ visitors
visitors upon opening. Each hour, the number of visitors increases at a rate of 1.2%
due to a special coupon.
To the nearest whole number, predict how many visitors the amusement park will have after 3 hours of being open.
__ visitors
Answers
GPT-4o mini
To calculate the number of visitors after 3 hours, we can use the formula for exponential growth:
\[
V(t) = V_0 \times (1 + r)^t
\]
where:
- \( V(t) \) is the number of visitors at time \( t \),
- \( V_0 \) is the initial number of visitors (350),
- \( r \) is the growth rate (1.2% or 0.012),
- \( t \) is the time in hours (3 hours).
Plugging in the values:
\[
V(3) = 350 \times (1 + 0.012)^3
\]
\[
V(3) = 350 \times (1.012)^3
\]
Now, calculate \( (1.012)^3 \):
\[
(1.012)^3 \approx 1.036432
\]
Now, substitute this back into the equation:
\[
V(3) \approx 350 \times 1.036432
\]
\[
V(3) \approx 362.75
\]
Rounding to the nearest whole number:
\[
V(3) \approx 363
\]
Therefore, the predicted number of visitors after 3 hours is **363** visitors.
\[
V(t) = V_0 \times (1 + r)^t
\]
where:
- \( V(t) \) is the number of visitors at time \( t \),
- \( V_0 \) is the initial number of visitors (350),
- \( r \) is the growth rate (1.2% or 0.012),
- \( t \) is the time in hours (3 hours).
Plugging in the values:
\[
V(3) = 350 \times (1 + 0.012)^3
\]
\[
V(3) = 350 \times (1.012)^3
\]
Now, calculate \( (1.012)^3 \):
\[
(1.012)^3 \approx 1.036432
\]
Now, substitute this back into the equation:
\[
V(3) \approx 350 \times 1.036432
\]
\[
V(3) \approx 362.75
\]
Rounding to the nearest whole number:
\[
V(3) \approx 363
\]
Therefore, the predicted number of visitors after 3 hours is **363** visitors.