Question

Currently, the number of pizzas sold by a restaurant is 87. It is estimated that the number of pizzas sold will increase by 5% each hour. Find the total number of pizzas sold at the end of 7 hours.

Answer 1

To calculate the total number of pizzas sold after 7 hours with a 5% hourly increase, apply the exponential growth formula P(t) = P0(1 + r)^t. Start with 87 pizzas and apply a growth rate of 5%, or 0.05, over 7 hours.

Step-by-step explanation:

The question relates to exponential growth in Mathematics, specifically related to a real-world application of a restaurant's pizza sales. To find the total number of pizzas sold at the end of 7 hours with a 5% increase each hour, we can use the formula for exponential growth:

P(t) = P0(1 + r)^t

where P(t) is the number of pizzas sold after t hours, P0 is the initial amount of pizzas sold, r is the growth rate per hour, and t is the number of hours.

1. Identify the initial number of pizzas sold (P0): 87 pizzas.
2. Determine the hourly growth rate (r): 5%, which is 0.05 as a decimal.
3. Calculate the number of pizzas sold after t hours, where t is 7.
   

Using the formula, we have:

P(7) = 87(1 + 0.05)^7 = 87(1.05)^7

Calculating the above expression gives us the total number of pizzas sold at the end of 7 hours.