Exponential Growth and Decay
Given y=6(0.91)^x, what is the rate of decay? Write your answer as a percent
9%
What is the value of e to five decimal places?
2.71828
Write log2(32)=5 as an exponential equation.
25=32
Expand log(xy^2)
logx +2logy
Solve for x .
16^(3x)=8
(Hint a^(x)=a^(y) impliesx=y )
x=1/4
Given an exponential function of the form y=ab^(x) , what condition must b meet for exponential growth?
b > 1
Evaluate e^-3 to four decimal places.
0.0498
Write (1/2)^(-4)=16 as a logarithmic equation
log_(1/2)16=-4
Condense 2loga + 1/2logb
loga^2b^(1/2)
Solve for x
6^(2x)=75
Round to four decimal places.
x=1.2048
A $12,000 car depreciates 9% each year. What is the value of the car after five and a half years? Round to the nearest hundredth.
$7143.46
If you invest $10,000 with an interest rate of 5%, compounded quarterly, how much money will you have after 5 years? Round to the nearest hundredth.
$12,820.37
Evaluate log_2 64 .
6
Evaluate lne^5.896 .
5.896
Solve for x
lnx-ln2=3 .
Round to three decimal places.
x \approx 40.171
Given y= 500(1.04)^x find the y-intercept. Write your answer as an ordered pair, e.g. (x,y).
(0,500)
If you invest $5675.45 at a rate of 6%, compounded weekly, how much money will you have after 10 years? Round to the nearest hundredth.
$10,867.14
Given y=-ln(x) + 2 , find the value of y when x=e .
y=1
Expand log(xyz)^5 .
5logx+5logy+5logz
An initial investment of $350 dollars is compounded continuously at a rate of 4% over 8 years. How much is it worth now? Round to four decimal places.
$481.99
A baseball card bought for $50 increases in value by 3% each year. How much is the card worth after three years? Round to the nearest hundredth.
$59.70
You invested $17,000, compounded continuously at a rate of seven percent. How much will it be worth 16 years? Round to the nearest hundreth.
$52,102.52
Evaluate log_(3.1)90.23. Round to the nearest hundreth.
3.98
Condense logx + logy -2logz .
log(\frac{xy}{z^2})
Solve for x .
log 2 +log(x-3)=1
x=8