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Linear Functions
Logs
Exponential Functions
Compound Problems
Double and Half Life
100
if x=12, evaluate f(x) = 7 – (106/x)
-11/6
100
Solve for x: ln(x) - ln(4) = 2 ln(x) - ln(16)
x=4
100
Evaluate the following: e2 Ln(4) - ln(16)
1
100
A bank pays interest at the nominal rate of 1.3% per year. What is the effective annual rate if compounding is: Annually Monthly
Annually: 1.3% Monthly: 1.31%
100
Find the time needed for the turtle population described by the function P= 175(1.145)^t to double its initial size.
5.119 years
200
The US population , P, in millions, is currently growing according to the formula P=299e^0.009t = 350 Where t is in years since 2006. When is the population predicted to reach 350 million?
2024
200
Solve for x using logs: 2^x = 11
3.459
200
Find g(t)=ab^t if g(10)=50 and g(30)=25
Q = 70.711(0.966)^t
200
What is the effective annual rate of an account that pays interest at the nominal rate of 8% per year, compound daily?
8.32%
200
A population of 500 doubles in size every 15 years, what is the rate of growth?
4.7%
300
Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. If W(n) models the amount of water Andrei uses, and n represents the number of marbles, what is the glass tank's volume? W(n)=32−0.05n
32
300
Solve for x 5e^(2x) = 50
4.192
300
Q(t)=2300(1+0.23)^3 What is the starting value?
2300
300
Explain this formula in words Q(t)=120(1+0.45)^(t/5)
Starting value is 120 The function has a 45% rate of change and compounds once every 5 years
300
If 17% of a radioactive substance decays in 5 hours, what is the half-life of the substance?
0.231
400
Write a formula for the price p o a gallon of gas in t days if the price is $2.50 on day t=0 and the price is: a. Increasing by $0.03 per day b. Decreasing by $0.07 per day c. Increasing by 2% per day d. Decreasing by 4% per day
a. Since the rate of change is constant, the formula is the linear function p = 2.50 + 0.03t. b. Since the rate of change is constant, the formula is the linear function p = 2.50 − 0.07t. c. Since the percent rate of change is constant, the formula is the exponential function p = 2.50(1.02)t . d. Since the percent rate of change is constant, the formula is the exponential function p = 2.50(0.96)t .
400
Solve for 3x: log2(8) = x
9
400
Igbo uploaded a funny video of his cat onto a website. The relationship between the elapsed time, d, in days, since the video was first uploaded, and the total number of views, V(d) that the video received, is modeled by the following function. V(d)=10^(​1.5d) How many days will it take for the video to receive 1million views?
4
400
Rank the following three bank deposit options from best to worst. 1. Bank A : 7% compounded daily 2. Bank B: 7.1% compounded monthly 3. Bank C: 7.05% compounded continuously
B - C - A
400
The price P(t) = 5(2)t7of a good is rising due to inflation, where t is time in years. What is the doubling time?
7