Linear vs. Exponential
parent function y = ab^x
Growth
Decay
Compound Interest
100
exponential functions will always grow or decay _______ than linear functions over time
faster
100
Identify a and b for the function f(x) = 13(2)x
a = 13; b = 2
100
What range of values for b indicate exponential growth?
b>1
100
What range of values for b indicate exponential decay?
b<1
100
Why does compounded interest pay out more total interest than simple interest?
With compounded interest, your interest also earns interest because it is added to the principal.
200
Constant difference is to linear function as _________ is to exponential function
common ratio
200
If a volume is quadrupling with each successive step, what is the value of b?
4
200
The town of Madison has a population of 25000. The population is increasing by a factor of 1.12 each year. Write a function that gives the population P(t), in Madison t years from now.
y = 25000(1.12)t
200
A car depreciates 20% in value each year. What is the value of a 10-year old car sold at a manufacturer's suggested retail price (MSRP) of $35,799? (round to the nearest dollar)
$3844
200
Find the quarterly interest rate AS A DECIMAL when the annual interest rate is 5%
.0125
300
exponential
300
Fill in the blanks: Plan _____ starts with fewer memberships; the number of memberships for Plan _______ is increasing at a faster rate than the other Plan
1; 1
300
Chicago had a population of 2500000. The population is increasing by 3% each year. Write a function that gives the population P(t), in Chicago t years from now.
y = 2500000(1.03)t
300
An endangered species currently has 250 known living specimens. Given a 60% annual decrease, after how many years will the species become extinct (<1 known living specimen)?
7 years
300
Write the equation for an account with initial balance of $400 earning an annual interest rate of 3% compounded monthly.
y = 400(1.0025)12t
400
neither
400
Why does the parent function not have an exponent of x - 1 like a geometric sequence explicit formula?
Parent functions are based on the initial value when x = 0, NOT the first term when x = 1
400
How many rabbits will live in a forest in 18 months if the initial forest population is 18 and the population triples every other month (assuming no rabbits die or migrate)?
354294 rabbits
400
A medication with an initial concentration of 1.5 milligrams per liter is administered to a patient, and the decay rate of the drug is 10% per hour. Write an equation that can be used to model the concentration, C, of the drug in the patient’s body as a function of time, t, in hours since the drug was administered.
C(t) = 1.5(.9)t
400
Write the equation for an account with initial balance of $8500 earning an annual interest rate of 4% compounded daily. (round the rate to the nearest millionth)
y = 8500(1.000111)360t
500
For which domain values will f(x) = g(x) given f(x) = 2x and g(x) = x + 1
x = 0 and x = 1
500
You MUST show work
B
500
A bacteria population grows from 30 to 15000 in 2 hours. Assuming the rate does not change, how many bacteria were present after 1 hour (rounded to the nearest whole number)?
671 bacteria
500
A car depreciates 20% in value each year. A 6-year old car is worth $12,500. What was its value when purchased? (round to the nearest dollar)
$47,684
500
How much more interest will an account with an initial balance of $1000 earn in one year if interest is compounded quarterly versus simple annual interest if it earns $50 in simple annual interest in one year?
$0.95