Question

lets practice!

1. given the exponential function ( y = 3(5)^x )

a. state the starting value.
b. state the growth/decay factor.
c. is the function growing or decaying?
d. describe in words what this function is doing. refer to the language in the intro activity.
e. what is the result if ( x = 3 )?

1. given the exponential function ( y = 32(0.25)^x )

a. state the starting value.
b. state the growth/decay factor.
c. is the function growing or decaying?
d. describe in words what this function is doing. refer to the language in the intro activity.
e. what is the result if ( x = 2 )?

Explanation:

Step1: Identify starting value (1a)

The starting value of an exponential function $y = a(b)^x$ is $a$. For $y=3(5)^x$, $a=3$.

Step2: Identify growth factor (1b)

The base $b$ is the growth/decay factor. For $y=3(5)^x$, $b=5$.

Step3: Classify growth/decay (1c)

If $b>1$, it is growth. $5>1$, so growing.

Step4: Describe the function (1d)

Start at 3, multiply by 5 each time $x$ increases by 1.

Step5: Calculate for $x=3$ (1e)

Substitute $x=3$: $y=3(5)^3 = 3\times125 = 375$.

Step6: Identify starting value (2a)

For $y=32(0.25)^x$, the starting value $a=32$.

Step7: Identify decay factor (2b)

The base $b=0.25$ is the decay factor.

Step8: Classify growth/decay (2c)

If $0

Step9: Describe the function (2d)

Start at 32, multiply by 0.25 each time $x$ increases by 1.

Step10: Calculate for $x=3$ (2e)

Substitute $x=3$: $y=32(0.25)^3 = 32\times0.015625 = 0.5$.

Answer:

1. a. 3

b. 5
c. Growing
d. Starts at 3, multiplies by 5 for each increase of 1 in $x$.
e. 375

1. a. 32

b. 0.25
c. Decaying
d. Starts at 32, multiplies by 0.25 for each increase of 1 in $x$.
e. 0.5