Exploring Exponential Models
Determine whether the function shows exponential growth or decay, and find the growth/decay factor y-intercept.
y=0.8(0.125)x
- Exponential decay
- Decay factor: 0.125
- y-intercept: (0, 0.8)
Considering the parent function y=bx, identify the transformation of y=-2(5)x=3.
- Reflected accross the x-axis.
- Vertical stretch by a factor of 2.
- Translated left 3 units.
If no base is written on a logarithim, what is the base assumed to be?
The base is assumed to be 10 (a common log).
Write 4logm - logn as a single logarithim.
log(m4)/(n)
Solve 43x = 64.
x = 1
Determine whether the function shows exponential growth or decay, and find the growth/decay factor y-intercept.
y=0.45(3)x
- Exponential growth
- Growth factor: 3
- y-intercept: (0, 0.45)
Find the value of e5.
- e5 ≈ 148.41
What is the logarithmic for of 103=1000?
The logarithmic form of 103=1000 is log1000=3.
Expand log5rs.
log5r + log5s
Solve 252x+1 = 144. Round to the nearest ten-thousandth.
x ≈ 0.2720
Write an exponential function to model the situation, and find the amount for the given time.
A population of 130,000 grows 2.2% per year for 10 years.
- y=130,000(1.022)10
- 161, 604
Find the value of 14e10.
- 14e10 ≈ 308370.52
Evaluate log39.
log39=2
Expand log(a2b3)/(c4).
2loga + 3logb - 4logc
Solve 3logx = 1.5.
x = √(10) or ≈ 3.162
You deposit $2500 in a savings account. The account pays an annual interest of 5%. How much will be in the account after 5 years?
There will be $3190.70 in the account.
You deposit $3200 in an account that pays an annual interest of 6% compounded continuously. How much will have after 3 years?
There will be about $3831.10 in the account.
Evaluate log32(1/16).
log32(1/16)=(-4/5)
Use the Change of Base Formula to find the value of log333.
log333 ≈ 3.183
Solve log2x+logx = 11.
x ≈ 223606.80
You deposit $2000 in a savings account. The account pays an annual interest of 3%. Assuming you never deposit or withdraw anything, how many years will it take for the account to have $2800?
The account will have $2800 in about 12 years.
You deposit $2000 in an account. The account pays 10% annual interest compounded continuously. How much will be in the account 6 years later?
There will be about $3644.24 in the account.
What are the points of y=log4=4x if -1, 0, and 1 are y values?
- (1/4, -1)
- (1, 0)
- (4, 1)
Use the properties of logarithims and the Change of Base Formula to evaluate log448 - 1/2log49.
log448 - 1/2log49 = 2
Solve log(7x+1) = log(x-2)+1.
x = 7