Exponential Relationships Review (A)

Make a Table and Is it Growth or Decay

100

y=3(0.6)^x

^{For -1, 0, 1, and 2}

(-1, 5)

(0, 3)

(1, 1.8)

(2, 1.08)

Decay Function

Domain: All real Numbers

Range: [0, ∞)

200

y= - 4(3.1)^x

^{-1, 0, 1, 2}

(-1, -1.29)

(0, -4)

(1, -12.4)

(2, -38.44)

Exponential Growth Function

Domain: All Real numbers

Range: [0, -∞)

300

y=2(3)^x 

-1, 0, 1, 2

(-1, 2/3)

(0, 2)

(1, 6)

(2, 18)

Growth

D: All Real numbers

R: [0, ∞)

400

 6(0.7)^x

^{-1, 0, 1, 2}

(-1, -8.57)

(0, -6)

(1, -4.2)

(2, -2.94)

Decay

D: All Real

R: (-∞, 0]

Sketch the Graph and Identify the Start Value

100

f(x) = - 24(1.2)^x

^{Sketch the Graph and Identify the Start Value}

SV: -24

200

y= 63(⅞)^x

SV: 63

300

f(x)= - 12(.8)^x 

SV: -12

400

y= 18(1¾)^x

SV: 18

Write an Exponential Function for 2 points

100

(2,1000) and (3,100)

y=100000(.1)^x

200

(-2,4) and (-1,8)

y=16(2)^x

300

(1, 12) and (3, 108) 

y=4(3)^x

400

 (1, -28) and (2, -7)

y=-112(.25)^x

Exponential Words

100

A ball is dropped from a height of 30 feet. The function f(x) = 30(.92) ^x gives the height in feet of each bounce, where x is the bounce number. What will be the height of the 6th bounce to the nearest tenth of a foot? Show your work. 

18.2ft

200

You have $1000 in your savings account that is earning interest. The function f(x) = 1000(1.018) ^x gives the total amount in savings after each year, where x is the number of years. What will be the total in the account after 18 years? 

$1378.67

300

 A car with an initial value of $42,000 is decreasing in value at a rate of 9% each year.

       a) Write the equation that models the situation.

       b) Use the equation to find the approximate value of the car in 18 years.

y=42000(.91)^x

$7691.20

400

A baseball card was bought in 1963 for $0.30 and has been increasing in value at a rate of 6% each year.

       a) Write the equation that models the situation.

       b) Use the equation to find the approximate value of the card in 2018.

y=.30(1.06)^t

$7.40

500

The population of a town is 12,120 and is decreasing at a rate of 1.2% per year.

         a) Write the equation that models the situation.

         b) Use the equation to find the approximate population of the town in 120 years.

y=12120(0.988)^t

2847

Amanda is considering 2 jobs, they offer the salaries listed below. Job A: $45,000 for the first year with a $6000 raise each year.Job B: $35,000 for the first year with a 18% raise each year.

100

a) Is the salary plan for Job A modeled by a linear function or an exponential function? Explain your Reasoning

Linear

200

Is the salary plan in Job B modeled by a linear function or an exponential function? Explain your reasoning.   

Exponential

300

Write an equation that models the salary for Job A.    

45000+5000(t) = y

400

Write an equation that models the salary for Job B. 

y=35000(1.18)^t