General Questions
Applying Exponential Equations
Initial Amount, Decay Rate, and Growth Rate
Writing Exponential Functions
Exponential Graphs
100
Is the following growth or decay: f(x) = 2^x
What is growth
100

The number of bacteria in an experiment is presently 38,300. Each hour, the cells split, doubling the number of bacteria present. How many millions of bacteria are present after 9 hours?

Approximately 19 million bacteria. (19,609,600) 

100

Use y = 250(1.2)^t What is the initial value?

What is 250

100

Write an exponential growth function to model the situation. A population of 422,000 doubles each year.

What is f(x) = 422,000(2)^x

100

Given f(x) = 2(3)x

What is the y-intercept?

(0, 2)

200
Is the following growth or decay: f(x)=100*(0.5)^x
What is decay
200

A child puts 1,900 pennies in their piggy bank. Once a week, their brother sneaks in to steal money, leaving only 1/4 of the pennies behind. How many pennies will the poor child be left with after 3 weeks? 

29

200

Use y = 250(1.2)^t What is the multiplier?

What is 1.2

200

The population of Baconburg starts off at 20,000. Each summer, the swamp monster gets hungry and eats half of them. Write an exponential model.

What is f(10) = 20,000(0.05)^x

200

Given f(x) = 2(3)x

What is the asymptote?

y = 0

300

what does x0 equal?

1

300
The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. What will the population of the town be in 5 years?
Approximately 42, 499 People
300

Use y = 250(1.2)^t What is the growth rate in percent?

What is 20%

300

The Hippityhoppity bunny decided to have a family reunion at the Magic Forest every 5 years. During the second reunion the family discovered that the number of family members was 154 and was growing at an annual rate of 3.2%. Write an equation to model the growth of the bunny family.

What is f(x) = 154(1.032)^x

300

Given f(x) = 2(3)x

What is the domain?

all real numbers

400

What is the difference between linear and exponential functions, regarding how the y values change?

Linear = repetitive adding

Exponential = repetitive multiplication

400
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. How much will the car be worth in 8 years?
$4,076.64
400

y = 9.8(0.35)^t What is the decay rate in percent?

What is 65%

400

The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.

What is y = 2500(.985)^x

400

Given f(x) = 2(3)x

What is the range?

y > 0

500

What happens if you add a value to an exponential function? 

For example, y = 3(2)x + 5

shifts the graph up

500
The value of a stock when purchased is $10 a share. However, over the past 5 days the price went down at a constant rate of 4%. How much is the stock worth now?
$8.15
500

Given the two points (0, 4) and (1, 1), what is the decay factor (b)?

0.25

500

The squid in The Magic Forest Lake were declining at an annual rate at 5.5%. Their current number is estimated at 50,000. Write an equation to predict the number of squid in the lake in 10 years.

What is f(10) = 50000(.945)^10 and 28,398 squid

500

define asymptote

a line that the graph approaches but never touches

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