Interpreting/Evaluate
Using Technology
Writing Equations
Review
100
This function can be used to determine the number of bacteria in a culture h hours after the culture was started.
f(h) = 10(3)h
Which statement best describes the meaning of the equation f(2) = 90
A. It gives the number of bacteria in the culture after 2 hours.
B. It gives the number of bacteria in the culture after 3 hours.
C. It gives the number of bacteria in the culture after 45 hours.
D. It gives the number of bacteria in the culture after 90 hours.
A. It gives the number of bacteria in the culture after 2 hours.
100
Which of these represents an exponential function that has a y-intercept of 2 and passes through the point (4, 32/625)?
A. y = 4/25(2)x
B. y = 2(2/5)x
C. y= 2(4/25)x
D. y = 0.4(2)x
B. y = 2(2/5)x
100
Consider this sequence of numbers. 6, 12, 24, 48, 96, ... Which function represents this sequence?
A. f(n) = 3(2)n
B. f(n) = 3(2n)
C. f(n) = 4n+2n
D. f(n) = 6(n)2
A. f(n) = 3(2)n2
100
Given the table below. What is the average increase in profit between 100 and 300?
x y
0 0
100 2000
200 3000
300 3500
400 4250
7.50
200
The exponential function h(t) = 80(1.04)t models the relationship between the value, , in thousands of dollars, of the house and the number of years, , since Mr. Nihlen bought the house.
Which statement correctly interprets this model?
A. The value of the house increases by 1.04% each year.
B. The value of the house increases by 4% each year.
C. The value of the house increases by $1,040 each year.
D. The value of the house increases by $4,000 each year
B. The value of the house increases by 4% each year.
200
A city has current population of 55,000, and it is growing at a rate of 2% each year. What is the approximate predicted population after 7 years?
63,178
200
The table below shows pairs of x and y values for a function of x.
x y
0 -1
1 -1/2
2 -1/4
3 -1/8
Write an equation to model the table.
f(x) = -1(1/2)x
200
What is the average rate of increase in website views from day 1 to day 6?
7
300
The value of a painting recently sold at an auction is expected to increase in value over time. The function v(t) = 12000(1.15)t represents the value of the painting, v(t) , at time t, where is the measure in years since the painting was sold at the auction.
Which of the following statements provide a correct interpretation of the function representing the value of the painting? Select ALL that apply.
A. The painting was sold at the auction 1.15 years ago.
B. The painting's value was 1.15 at the time it was sold at the auction.
C. Each year the painting increases its value by 15 percent.
D. The painting was sold at the auction 12,000 years ago.
E. The painting's value was 12,000 at the time it was sold at the auction.
F. Each year the painting increases its value by 12,000 percent.
C. Each year the painting increases its value by 15 percent.
E. The painting's value was 12,000 at the time it was sold at the auction.
300
Which equation BEST represents the graph?
A. y = -3x
B. y = 3-x
C. y = x-3
D. y = -x3
A. y = -3x
300
A glacier is 220 miles long. Its length is decreasing by 5% every 10 years. If f(x) = the glacier’s length in miles after x years, which function describes this situation?
f(x) = 220(0.95)x/10
300
A system of equations is shown below
f(x) = 3x-5
g(x) = 2(x-5) + 3
What is the smallest value of x such that f(x) is approximately equal to g(x)?
2.7
400
The population of bacteria M after x minutes is represented by the function M(x) = 51(1.03)x . The population of bacteria P after x minutes is represented by P(x) = 29(1.05)x . What is the approximate difference between the populations after 3 minutes?
A. 16
B. 19
C. 22
D. 25
C. 22
400
At a school dance, there were 2 people on the dance floor when the music started. After that, the number of people dancing increased as shown in the table.
Assume that the pattern in the table continues. Write an equation can be solved for t, the time in minutes when the number of people dancing will reach 200?
200 = 2(3)t
400
Jason puts $15,000 in an investment account that pays him 2% annual interest. Write an equation represents the value of the account, V, after x years?
y = 15000(1.02)x
400
What is the range of the function f(x) = 3(0.27) ?
A
500
The function below represents the amount of caffeine in a person’s body t hours after drinking a cup of coffee. f(t) = 95(0.89) After drinking a cup of coffee, about how many hours would it take for half of the caffeine to leave a person’s body?
A. 1 hour
B. 3 hours
C. 5 hours
D. 6 hours
D. 6 hours
500
Solve -2(1/3)x-1 + 3 = 7(2)x-6 - 4
Use desmos and round answer to nearest thousandth.
-0.127 and 5.998
500
A scientist placed 6 bacteria into a petri dish. The number of bacteria in the petri dish doubled every 10 hours. Which equation models the number of bacteria, y, present in the sample after x hours?
D
500
The table below shows how the expected value of a certain autographed book varies with time.
Is the autographed book's expected value a linear or exponential function of time, and why?
Exponential - increases by 5% (multiply by 1.05)