Behavior
Which equation is most appropriate for modeling this data? (Image #1)
a. y = 64 (1.25)^x
b. y= 79 (1.25)^x
c. y= 79 + 1.25x
d. y= 64 + 22x
C
Here are equations defining three exponential functions f, g, and h. Which of these functions grows least quickly?
f(x) = 100 (3)^x
g(x) = 100 (3.5)^x
h(x) = 100 (4)^x
f(x)
The dollar value of a car is a function, f, of the number of years, t, since the car was purchased. The function is defined by the equation
f(t) = 12000 (3/4)^t
How much was the car worth when it was purchased?
$12,000
The function f represents the amount of medicine, in mg, in a person's body t hours after taking the medicine. Image #5 is the graph of f.
How many mg of the medicine did the person take?
80 mg
Automobiles start losing value, or depreciateing, as soon as they leave the car dealership. Five years ago, a family purchased a new car the cost $16,490.
If the car lost 13% of its value each year, what is the value of the car now?
About $8,218.96, or
16490 (0.87)^5
A bank account has a balance of 1,000 dollars. It grows by a factor of 1.04 each year.
Write an equation defining f.
y = 1000 (1.04)^x
Here are equations defining three exponential functions f, g, and h. Which of these functions grows most quickly? (Image #2)
f(x) = 100 (3)^x
g(x) = 100 (3.5)^x
h(x) = 100 (4)^x
h(x)
The dollar value of a car is a function, f, of the number of years, t, since the car was purchased. The function is defined by the equation
f(t) = 12000 (3/4)^t
What is f(2)?
$6,750
The function f represents the amount of medicine, in mg, in a person's body t hours after taking the medicine. Image #5 is the graph of f.
Write an equation that defines f.
f(t) = 80 (0.5)^t
From 2005 to 2015, a population of P lions is modeled by the equation P=1500 (0.98)^t, where t is the number of years since 2005.
What is happening to the population of lions over this decade?
Lion population is decreasing because 0.98 < 1.
Decreasing by 2% each year because 0.98 = 1 - 0.02.
After its second bounce, a ball reached a height of 80 cm. The rebound factor for the ball was 0.7.
From approximately what height, in cm, was the ball dropped?
a. 34 c. 115
b. 49 d. 163
163
Here are equations defining three exponential functions f, g, and h. The three graphs in image #2 represent f, g, and h. Which graph corresponds to each function?
f(x) = 100 (3)^x
g(x) = 100 (3.5)^x
h(x) = 100 (4)^x
A - h(x)
B - g(x)
C - f(x)
The dollar value of a car is a function, f, of the number of years, t, since the car was purchased. The function is defined by the equation
f(t) = 12000 (3/4)^t
About when was the car worth $6,000?
About 2.4 years
The function f represents the amount of medicine, in mg, in a person's body t hours after taking the medicine. Image #5 is the graph of f.
After 7 hours, how many mg of medicine remain in the person's body?
0.625 mg
From 2005 to 2015, a population of P lions is modeled by the equation P=1500 (0.98)^t, where t is the number of years since 2005.
About how many lions are there in 2015?
1500 (0.98)^10, or
about 1,226 lions
Image #6 shows the number of people, n, who went to see a musical on the dth day of April.
What is the average rate of change for the number of people from day 1 to day 7?
31 people per day
Image #3 shows graphs of three exponential equations. Match each equation to its graph.
A. y = 20 (3)^x
B. y = 50 (3)^x
C. y = 100 (3)^x
A - M
B - L
C - K
Image #4 is a graph of p, an insect population, w weeks after it was first measured. The population grows exponentially.
What was the population when it was first measured?
300
Lin opened a savings account that pays 5.25% interest annually and deposited $5,000.
If she makes no payments and no withdrawals for 3 years, how much money will be in her account?
About $5,829.57
A bank pays 8% nominal annual interest, compounded at the end of each month. An account starts with $600, and no further withdrawals or deposits are made.
What is the monthly interest rate?
8/12%, or about 0.67%
Image #7 is a graph of the function f defined by
f(x) = a (b)^x
Select all possible values of b.
1 1/2 9/10 1
1/10 1.3 18/5
1/10 1/2 9/10
Image #4 is a graph of p, an insect population, w weeks after it was first measured. The population grows exponentially.
What is the weekly factor of growth for the insect population?
3
Image #4 is a graph of p, an insect population, w weeks after it was first measured. The population grows exponentially.
Write an equation relating p and w.
p = 300 (3)^w
A person loans his friend $500. they agree to an annual interest rate of 5%.
Write an expression for computing the amount owed on the loan, in dollars, after t years if no payments are made.
500 (1.05)^t
A bank pays 8% nominal annual interest, compounded at the end of each month. An account starts with $600, and no further withdrawals or deposits are made.
Write an expression for the account balance, in dollars, after t years.
600 (1 + 0.08/12)^12t