Exponential Growth & Decay
Annual Interest
Evaluating Logs
Log Properties
Solving Equations
100
Find the y-intercept and write as an (x,y)-coordinate:
y=1.19*(4)^x
(0,1.19)
100
Convert the percent value to a decimal: 7.4%
0.074
100
Evaluate the logarithm:
log_6 216
log_6 216=3
100
Rewrite as a single logarithm:
log_2 7 + log_2 9
log_2 63
100
Solve the following equation:
2^(2x)=16
x=2
200
What is the percent change for the function below?
y=45(0.33)^x
-67%, or 67% decrease
200
What is the annual rate of interest, written as a percentage, of the savings account modeled by this equation?
A(t)=45.1(1.072)^t
7.2%
200
Evaluate the logarithm:
log_7 frac{1}{49}
log_7 frac{1}{49}=-2
200
Rewrite as a single logarithm:
2log y - log 6
log frac{y^2}{6}
200
Solve the following equation:
9^(n-1)=frac{1}{3^n}
n=frac{2}{3}
300
A $14,200 van depreciates in value by 7% every year. Find the value of the van after 9 years. Round to the nearest cent.
$7389.84
300
What is the equation of the form
A(t)=P(1+r/n)^(nt)
that matches this situation?
You put $3000 into a college savings account. The account pays 5.4% interest annually, compounded monthly.
A(t)=3000(1+0.054/12)^(12t)
or
A(t)=3000(1.0045)^(12t)
300
Evaluate the logarithmic expression:
log_16 2 + log_16 32
log_16 2 + log_16 32=frac{3}{2}
300
Evaluate the logarithm (rounded to the nearest hundredth):
log_5 17
log_5 17=1.76
300
Solve the following equation (with answer rounded to the nearest hundredth):
e^(3x)=25
x=1.07
400
In 1978, a Chewbacca figurine was bought for $2.50 and has appreciated in value by 22% each year. Find the value of the figurine in 2018. Round to the nearest cent.
$7117.59
400
In 2018, if you put $2500 into a savings account that pays 6.4% interest annually and is compounded continuously, how much money will be in the account in 2022 (rounded to the nearest cent)?
$3229.38
400
Evaluate the logarithm:
log_625 frac{1}{125}
log_625 frac{1}{125}=-frac{3}{4}
400
Expand the logarithm fully:
ln (3x)^5
5ln 3 + 5ln x
or
ln 243 + 5ln x
400
Solve the following equation (with answer rounded to the nearest hundredth):
ln x - ln 3 = 4
y=163.79
500
What is the equation of the form
y=ab^x
that matches this graph?
y=2(1/2)^x
500
With an initial deposit of $2308.52, you opened a savings account in 2015 that paid 4.1% interest annually, compounded weekly. How much money will be in the account in 2032 (rounded to the nearest cent)?
$4633.59
500
Evaluate the logarithmic expression:
log_27 frac{4}{5} + log_27 frac{5}{12}
x=-frac{1}{3}
500
Expand the logarithm fully:
log_3 sqrt(frac{m}{n})
frac{1}{2}log_3 m - frac{1}{2}log_3 n
500
Solve the following equation. Also, list any extraneous solutions:
2 log x - log 4 = 4
x=200
(extraneous solution: x = -200)