Exponential Graphs Warm Up Solve Find the Vertex

Exponential Graphs

Warm Up Solve: Find the Vertex:

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

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

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

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

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

Continued….

Graph: x y -2 0. 25 -1 0. 5 0 1 1 2 2 4 HA: y = 0 Domain: Range:

Graph: Decreasing! x y -2 4 -1 2 0 1 1 0. 5 2 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 l l

Graph: Left 1 Down 3 Domain: Range:

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

Graph: Is the inverse of Domain: Range:

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

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

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

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

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

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: l How many infected people are there initially? l 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. 71828…

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? l One million dollars at the end of the month. l 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 nth day. More Profitable