Exponential Graphs. Warm Up Solve: Find the Vertex:

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Presentation transcript:

Exponential Graphs

Warm Up Solve: Find the Vertex:

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: xy HA: y = 0 Domain: Range:

Graph: xy Decreasing! Domain: Range: HA: y = 0

Graph: Domain: Range: HA: y = 0

Graph: HA: y = 2 Domain: Range:

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

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

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

Natural exponential function

Graph: Domain: Range: Left 1 Down 3

Logarithmic Function It’s the inverse of the exponential function Switch the x’s and the y’s!

Graph: Domain: Range: Is the inverse of Domain: Range:

Graph: Domain: Range: Up 3 from previous example!

Graph: Domain: Range: Left 4 from Original Example!

Graph: Domain: Range: Right 2 from Original Example!

Graph: Domain: Range: Reflected over y-axis.

Graph: Domain: Range: Reflected over x-axis.

Compound Interest

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: annuallyn = 1 quarterlyn = 4 monthlyn = 12 dailyn = 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 = …

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

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, 2 n cents on the n th day. More Profitable