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:

 

amplitude

period

horizontal translation

vertical translation

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.