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

1 answer

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.