8 1 Exponential Growth Exponential Function Exponential function

8. 1 Exponential Growth

Exponential Function �Exponential function- contains the expression bx where the base “b” is a positive number other than 1. �Asymptote- a line at a graph approaches as you move away from the origin.

Exponential Growth �y = 3 x

Investigation Graph and. Compare the graphs with the graph of y = 2 x. 2) Graph and. Compare the graphs with the graph of y = 2 x. 3) Describe the effect of “a” on the graph of when “a” is positive and when it is negative. 1)

Exponential Growth �Exponential growth function: a graph in the form y = abx, when a>0 and b>1 �General exponential function ; “h” translates the graph horizontally and “k” translates the graph vertically

Examples: 1) Graph the functions a) b)

Examples: 2) Graph. State the domain and range. 3) Graph and range. . State the domain

Using Exponential Growth Models �When a real-life quantity increases by a fixed percent each year (or other time period) modeled by where a is the initial amount, r is the percent increase. “ 1+r” is called the growth factor

Example 4) In 1980 about 2, 180, 000 US workers worked at home. During the next ten years, the number of workers at home increased 5% per year. a) Write a model giving the number w (in millions) of workers working at home t years after 1980. b) Graph the model. c) Use the graph to estimate the yer when there were about 3. 22 million workers who worked at home.

Example: 5) In 1990 the cost of tuition at a state university was $4300. During the net 8 years, the tuition rose 4% each year. a) Write a model tat gives the tuition y (in dollars) t years after 1990. b) Graph the model.

Compound Interest �Where P is the initial principal; r is the annual rate (expressed as a decimal) compounded n times per year, A is the amount in the account after t years

Example: 6) You deposit %1500 in an account that pays 6% annual interest. Find the balance after 1 year if the interest is compounded a) annually b) semiannually c) quarterly

Example: 7) You deposit $2000 to an account that pays 8% annual interest. How much more does the account earn in one year if the interest is compounded monthly rather that annually?