Name that a value
Name that b value
Exponential Equations
Solve that
Percent Problems
100
What is the initial value in the following function:
f(x) = 1/2*(3/4)^x
1/2
100
What is the growth factor in the following equation:
f(x) = 3*2^x
2
100
There are 50 bacteria in a petri dish at the beginning of a science lab. Every hour, each bacterium splits into three bacteria. Write an equation that represents the number of bacteria, n, after t hours.
n = 50 *(3)^t
100
The amount of bacteria in a petri dish is 100. The bacteria population will double every hour. How many bacteria will be in the dish after 2 hours? Show or explain your work.
100*2^2=400
Or
100 X 2 X 2 = 400
400
100
A student takes a test that is 50 questions. The student gets 80% of the questions correct. How many questions did he get right? Show or explain you reasoning.
0.80 x 50 = 40
40 questions correct.
200
A car's price p is a function of the number of years, t, since it was purchased. The function is
p(t) = 18,000*(4/5)^t
What is the "a" value of this function? What does it mean in this situation?
The "a" value is 18,000. It is the price of the car when it was first purchased.
200
Mold growth that covers an area of 64 square feet is treated so that the mold can die off. Every day, the amount of mold decreases by 1/9 of what is what the day before. What is the decay factor in this situation?
8/9
200
Brenda gets 100 dollars for her birthday. She spends 1/4 of the money the 1st week. Every week, she continues to spend 1/4 of the money she had the week prior. Write an exponential equation to represent this situation.
y=100*(3/4)^x
f(x) = 100 *(3/4)^x
200
Given the following equation
f(x)=6*(1/4)^x
find f(2). Show or explain your work.
6*(1/4)^2 = 0.375
200
The cost of a car that was initially $10,000 is now 20% more. What is the cost of the car now? Show or explain your work.
(1.20) x 10,000 = 12,000
or
10,000 + (0.20) 10,000 = 12,000
300
What is the a value of this function?
3
300
Which of these functions would have a b value that is less than 1? Explain how you know.
K(x) because it is the only decreasing
300
The following equation represents the population in a given area x years after 1990:
f(x) = 90,000*1.5^x
What would f(-2) mean in this situation?
The population two years before 1990
300
The following equation represents the population in a given area x years after 1990:
f(x) = 90,000*1.5^x
What does f(-2) equal? Show or explain how you know
f(x) = 90,000*1.5^-2
40,000 people
300
A local clothing store is running a sale where all items are 30% off. If a shirt costs $45, what is the cost of the shirt after the sale? Show or explain your reasoning.
(0.70) x 45 = 31.50
OR
45 - (0.30) x 45 = 31.50
$31.50
400
The amount of medicine in a person's bloodstream is measured a few hours after they took the medication using a blood test. This situation can be modeled as a function of time using the following equation:
m(t) = 500 *(1/4)^t
What does the 500 tell us in this situation?
How much medicine is in their bloodstream when they take the blood test.
400
The amount of medicine in a person's bloodstream is measured a few hours after they took the medication using a blood test. This situation can be modeled as a function of time using the following equation, where t is the number of hours after the initial blood test:
m(t) = 500 *(1/4)^t
What does the 1/4 tell us in this situation?
That every hour, the amount of medicine in their bloodstream is going down by 3/4
OR
Every hour, the amount of medicine in their bloodstream is 1/4 of what it was the previous hour
400
Write the exponential equation that would represent this graph.
y = 4 * (1/2)^x
400
The following equation represents the population growth in t years after the year 2000.
f(t)=1000*(1.2)^t
Find the average rate of change between 2001 to 2003. Show or explain your work
(f(3) - f(1))/(3-1)
(1,728-1200)/2
264
400
The price of a new waverider is $17,000. The sales tax on the waverider is 7.8%. What is the total cost of the waverider including tax?
17,000 X 1.078 = 18,326
$18,326
500
If
g(x) = 90 *(1/2)^x
what can we say about the "a" value of f? Explain how you know.
The a value of f must be less than 90 because f has a lower y-intercept that g OR because f starts lower on the y-axis
500
The graph above shows the growth in a rabbit population over time. What is the growth factor? Show or explain your work.
sqrt(20000/200) =10
500
Write the exponential equation represented by this graph:
Show or explain your reasoning.
y = 1.5*3^x
500
The following graph represents the function f(x)
Using the graph, find f (3). Show or explain your work.
Use the equation
f(x) = 3 *2^x
3 *2^3 = 24
500
In 2011, the number of students at a community college was 20,000. In 2012, the number of students increased by 8%. In 2013, the number of students increased again from the previous year, this time by 5%. How many students are there in 2013? Show or explain your work
(20,000 x 1.08) x 1.05 = 22,680