Exponential Functions

Exponential Functions

​

Exponential functions have a variable as an exponent

Multiple Choice

Which of the following is an exponential function?

• $f\left(x\right)=x^2$

• $f\left(x\right)=3x^3$

• $y=x^3$

• $f\left(x\right)=3^x$

Exponential Functions

Multiple Choice

What is the initial value in

 $y=4\left(2\right)^x$  

• 4

• 2

• x

Multiple Choice

What is the y-intercept of

 $y=-2\left(7\right)^x$  

• (-2, 0)

• (0, 7)

• x

• (0, -2)

• (4, 2)

Multiple Choice

What is the starting amount in the problem

 $f\left(x\right)=300\left(1.05\right)^x$  

• 300

• 1.05

• x

• y

Multiple Choice

What is the growth or decay factor for the equation

 $f\left(x\right)\ =\ 25\left(4\right)^x$  

• 25

• 4

Exponential Growth vs Decay

Multiple Choice

What is

 $b^0$  

• -1

• 0

• 1

Multiple Select

Select the functions that are exponential growth.

• $y=-2\left(3\right)^x$

• $f\left(x\right)=3\left(1.09\right)^x$

• $f\left(x\right)=4\left(\frac{1}{3}\right)^x$

• $y=0.5\left(\frac{3}{2}\right)^x$

To find the value of b from scenarios (if we are INCREASING at a rate of 5%)

• Turn the percent to a decimal by moving the decimal 2 places left (.05)

• Add 1 to the decimal (1+.05 = 1.05)

To find the value of b from scenarios (if the rate we are DECREASING at 8%)

• Turn the percent to a decimal by moving the decimal 2 places to the left (.08)

• Subtract this value from 1 (1-.08 = .92)