In this lesson, we will learn how to apply the power, product, quotient, and chain rules for differentiation to business, economics, management sciences, social sciences, and life sciences.

Q1:

A population study on a conservation forest has determined that the population of a certain species of rabbits depends on the population of gray foxes in the same forest. If there are πΉ foxes in the forest, then the expected number of rabbits is given by 2,020β29β10πΉ+1ο¨, where 0β€πΉβ€500. Find the rate of change in the expected population of this species of rabbits with respect to the population of gray foxes when there are 200 gray foxes in the forest. Round your answer to the nearest whole number.

Q2:

A company manufacturing shoes makes $100,000 in total cumulative profit by the beginning of the year 2015. The companyβs total cumulative profit π‘ years from the beginning of the year 2015 is οΌ100+2π‘β12π‘οπο¨ο¦οο¦ο«ο thousand dollars.

Find the rate of change of the companyβs profit at the beginning of the year 2020. Round your answer to the nearest dollar.

Q3:

Consider a savings account with an annual interest rate of 5%, compounded continuously. The initial account balance is $12,000, and the balance in dollars after π‘ years is given by 12,000πο¦οο¦ο«ο.

Find the rate of change of the account balance with respect to time π‘ in 5 years and in 10 years. Round your answers to the nearest cent.

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