Exponential Graphs Section 3.1

Objective Draw Exponential Graphs Draw Logarithmic Graphs Find Compound Interest Find Continuous Interest

Relevance Exponential functions are useful in modeling data that represent quantities that increase or decrease quickly. For example, an exponential function can be used to model the depreciation of a new vehicle.

Warm Up Solve: Find the Vertex:

Why do complex conjugates come in pairs? Warm Up Why do complex conjugates come in pairs?  

Definition In an exponential function, the base is fixed and the exponent is a variable.

Exploration Using your GDC, graph the following exponential functions on the same screen:

Exploration What do you observe about the function as the base gets larger, and the exponent remains positive?

Exploration Using your GDC, graph the following exponential functions on the same screen:

Exploration… Using your GDC, graph the following exponential functions on the same screen:

Continued….

Graph: x y -2 0.25 -1 0.5 1 2 4 HA: y = 0 Domain: Range:

Graph: Decreasing! x y -2 4 -1 2 1 0.5 0.25 HA: y = 0 Domain: Range:

Graph: HA: y = 0 Domain: Range:

Graph: HA: y = 2 Domain: Range:

Graph: HA: y = -3 Domain: Range:

Graph: HA: y = -5 Domain: Range:

Graph: HA: y = 2 Parent Function Right 4 Up 2 Domain: Range:

Natural exponential function

Graph: Left 1 Down 3 Domain: Range:

Compound Interest

How many infected people are there initially? An infectious disease begins to spread in a small city of population 10,000. After t days, the number of persons who have succumbed to the virus is modeled by the function: How many infected people are there initially? How many people are infected after five days?

Compound Interest P = Principal r = rate t = time in years n = number of times it’s compounded per year Compounded: annually n = 1 quarterly n = 4 monthly n = 12 daily n = 365

Find the Final Amount: $8000 at 6.5% compounded quarterly for 8 years

Find the Final Amount: $600 at 9% compounded daily for 20 years

Find the Final Amount: $300 at 6% compounded annually for 25 years

Compounded Continuously: P = Principal r = rate t = time in years E = 2.718281828…

Find the Final Amount: $2500 at 4% compounded continuously for 25 years

More Profitable One million dollars at the end of the month. Suppose your are offered a job that lasts one month, and you are to be very well paid. Which of the following methods of payment is more profitable for you? How much will you make? One million dollars at the end of the month. Two cents on the first day of the month, 4 cents on the second day, 8 cents on the third day, and, in general, 2n cents on the nth day. More Profitable