Use the following information to complete part A: A population of fruit flies starts with 6 flies. On day 4, the population has grown to 94 fruit flies.
A. Write an exponential growth function, y = aebt, to model the growth of the fruit fly population.
1. Describe the step-by-step process used to determine the function.
2. Create a table by applying the function from part A to show the estimated population for each day from 0 to 10 days.
3. Determine the day when the population will first exceed 1,000 fruit flies by applying the function, showing all steps and calculations.
Use the following information to complete part B: The depth of water at the end of a pier varies with the tides. On a particular day, the low tides occur at 2:00 a.m. and 2:00 p.m. with a depth of 2.1 meters. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 6.3 meters. A large boat needs at least 4 meters of water to be safely secured at the end of the pier.
B. Develop an exact trigonometric function that models the depth of water in meters t hours after midnight.
Note: An exact function does not use decimal approximations.
1. Describe the step-by-step process used to determine the exact function from part B, including a discussion on each of the following:
2. Calculate the time to the nearest minute that the boat can first be safely secured by using the function from part B. Explain step-by-step all mathematical calculations.