Lesson 8.1

 Exponential Function: a function that involves the expression b x where the base b is a positive number other than 1.  Asymptote: a line that a graph approaches as you move away from the origin.  Exponential Growth Function: a function of the form f(x) = ab x where a > 0 and b > 1.  Growth Factor: the quantity 1 + r in the exponential growth model y = a(1 + r) t where a is the initial amount and r is the percent increase expressed as a decimal.

A)B)

To graph a general exponential function, y = ab x-h +k, begin by sketching the graph of y = ab x. Then translate the graph horizontally by h units and vertically by k units.

Describe the translation on: A) B)

A) In the past 10 years, an initial population of 44 deer in a state park grew by about 8% per year. Write a model giving the number d of deer after t years. About how many deer were in the park after 5 years? B) In 1980 about 2,180,000 U.S. workers worked at home. During the next 10 years, the number of workers working at home increased 5% per year. Write a model giving the number w (in millions) of workers working at home t years after 1980.

Consider an initial principal P deposited in an account that pays interest at an annual rate r (expressed as a decimal) compounded n times per year. The amount A in the account after t years can be modeled by the equation:

You deposit $1400 in an account that pays 4% annual interest. Find the balance after 1 year if the interest is compounded with the given frequency: A) Annually B) Monthly C) Daily