MODELLING EXPONENTIAL FUNCTIONS WORKSHEET

Problem 1 :

The amount of money A accrued at the end of n years when a certain amount P is invested at a compound annual rate r is given by

A = P(1 + r)ⁿ

If a person invests $150 at 5% interest compounded annually, find the approximate amount obtained at the end of 5 years.

a)  $191     b) $4500     c) $1139   d) $900

Solution

Problem 2 :

The projected worth (in millions of dollars) of a large company is modeled by the equation

y = 246 (1.1)^x

The variable x represents the number of years since 1997. What is the projected annual percent of growth, and what should the company be worth in 2005?

a) 21%; $273.06 million         b) 21%; $629.28 million

c) 11%; $566.92 million         d) 11%; $510.74 million

Solution

Problem 3 :

You borrow $200 from a relative for six months. You agree to pay compound interest at the rate of 1% per month. How much interest will you pay your relative when you return the money at the end of the six months?

a) $11.66     b) $201.00     c) $210.00     [d)   $12.30

Solution

Problem 4 :

Which of the following accounts will yield the greatest amount of interest on an initial deposit of $500.00?

a) Account that pays 6% interest compounded annually for 3 years

b) Account that pays 4% interest compounded annually for 4 years

c) Account that pays 3% interest compounded annually for 5 years

d) Account that pays 5% interest compounded annually for 6 years

Solution

Problem 5 :

The population of Mexico in mid-1994 was 91,800,000. Its annual growth rate is 2.2%. Estimate its population in mid-2000.

Solution

Problem 6 :

Use any problem solving strategy to solve the following problem. The value of a house is expected to increase from its current value of $50,000 by 3% each year. What will the value of the house be after 3 years?

If you have $55,000 in 3 years, will you have enough to buy the house?

Solution

Problem 7 :

A position at a local company has a starting salary of $15,000. The salary is expected to increase by 5% each year. What will the salary be after 5 years?

Solution