Question

1. The department store’s annual profit from the sale of a certain toy is given by the function 8000 30,000(2) 0.4x y where y is the annual profit in dollars and x denotes the number of years the toy has been on the market. Calculate the store’s annual profit for (a) x = 3 (b) x = 5 (c) x = 15 2. It is estimated that the population P of a certain country is given by the function P(t) 4,000,000(1.02) r where t is the number of years after 1989. If this trend continues, what will the population be 20 years after 1989? 3. The projected population of a city is given by 20 125,000(1.11) t P , where t is the number of years after 1995. What is the projected population in 2015? 4. Suppose $900 is placed in a saving account that earns interest at the rate 4.5% compounded semiannually. (a) What is the value of the account at the end of five years? (b) If the account has earned interest at the rate of 4.5% compounded semiannually, what would be the value after five years?

Answer 1

Part A:

Given 900 dollars

Interest rate = 4.5%

Value at the end of 5 years

900 × 4.5% × 5 = $226.62

900 + 226.62 = 1,126.62

= 1,126.62 after 5 years

Part B: Given 900 dollars is placed in a saving account

interest rate = 4.5% semiannually (which means twice a year)

We need to find the value after 5 years

Since it's semiannually it's twice a year

5 × 2 = 10

900 × 4.5% (interest rate) × 10

900 × 4.5% × 10 = 510.29

510.29 + 900(intital amount) = 1,410.29

= $1,410.29 after 5 years