Growth and Decay
Is the following growth or decay: f(x)=100(0.5)t
Decay
Write an exponential growth function to model the situation. A population of 422,000 increases by 12% each year.
f(x) = 422,000(1.12)t
Any number to the power of 0 = ?
1
Write the exponent as a logarithm:
54 = 625
log5625 = 4
What are the formulas for Exponential Functions? How do you know if the function shows growth or decay?
f(x) = a(1+r)t and f(x) = a(1-r)t
If the number in the parentheses is greater than 1, the function shows growth.
If the number in the parentheses is less than 1, the function shows decay.
Is the following growth or decay: f(x)= 100(1.4)t
Growth
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?
$1751.21
In the graphs of the parent functions 2x and (1/2)x, what are the asymptotes?
y=0
Write the logarithm as an exponent:
log6(1/216) = 1/3
61/3 = 1/216
What is the formula used when compounding interest?
A = P(1 + r/n)nt
Use y = 250(1.2)t What is the initial amount?
250
The value of a stock when purchased is $10 a share. However, over the past 5 days the price went down at a constant rate of 4%. How much is the stock worth now?
$8.15
In a t-chart with the x-values of -1, 0, and 1, where can you find the y-intercept?
When x=0.
Evaluate the logarithm:
log2(32)
5
How do we convert the rate before we calculate an exponential (growth, decay, compounded interest, continuously compounded interest)?
Change it to a decimal by dividing the rate by 100.
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. How much will the car be worth in 8 years?
$4,076.64
Ms. Yawin invested $9,000 in an account that pays 6.5% annual interest. How much will be in the account after 8 years if the interest compounds quarterly?
$15,075.11
In the equation y = a * bx-h + k, which variable shows a movement up or down?
k
Evaluate the logarithm:
log1/5(125)
-3
What is the formula used when compounding interest continuously?
A = Pert
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the population of the town after 9 years.
Approximately 42,640 people
Bank of Colorado has an account that earns 1.5% interest, compounded continuously. If you invest $10,000, what is the value of the account after 4 years?
$10,618.37
In the equation f(x) = -(4)x+3 - 7, what are the transformations?
reflection over the x-axis, left 3, down 7
Evaluate log(1600) to the nearest tenth.
3.2
What is e approximately equal to?
2.71828...