Laws of Exponents
Equations with Properties of Exponents
Equations with different bases
Exponential Graphs
Word Problems
100
Simplify
(a^2b^3c)/(abc)
ab^2
100
Solve for x.
e^x=e^5
x=5
100
Rewrite 64 using base 2.
2^6
100
Determine the equation for this graph.
y=3^x
100
$1250 was put in an account with an annual 3% simple interest. How much interest will be in the account after 2 years?
$75.00
200
Simplify
(a^3a^5)/a^2
a^6
200
Solve for x.
112^(x+1)=112^9
x=8
200
Solve for x.
4^2=2^x
x=4
200
Describe the transformation going from
y=e^x to y=e^(x-1)+1
Shift right 1, up 1
200
A car was purchased for $32,000. It depreciates annually at a rate of 20%. How much will the value of the car be after 8 years? Round to the nearest cent.
$5368.71
300
Simplify. The final answer must have positive exponents.
(9a^3c^-3)/(27ab^-2c)
(a^2b^2)/(3c^4)
300
Solve for x.
e^x*e^3=e^(2x)
x=3
300
Solve for x.
125^x=625
x=4/3
300
The graph for y=3^x is shown as the dotted curve. What is the equation for the solid curve?
y=3^(x-2)
300
The half life of titanium-44 is 63 years. If there were initially 200 grams of titanium-44, how much of it will be left after 120 years? Round to the nearest tenth.
53.4 grams
400
Simplify and write in the a^b form.
(32*16)/4
2^7
400
Solve for x.
(1953^3)^12=1953^(9x)
x=4
400
Solve for x.
(3^x)^2=243
x=5/2
400
Sketch the graph for the function below. Clearly label f(0) and f(1).
f(x)=4^x
400
$4,500 was charged on a credit card with a 21% interest rate compounded daily. How much needs to be paid off after 3 months? Round to the nearest cent.
$4742.49
500
Simplify
(x^2y^3)^4/(x^5y^2z^-3)*(xyz^2)/1
x^4y^11z^5
500
Solve for x.
(2^e*2^3)^3=sqrt(2^x)
x=6e+18
500
Solve for x.
16^(2x)=64^e*64^3
(3e+9)/4 or (6e+18)/8
(Please simplify on the test)
500
The red curve is the graph of y=3^x . Determine the equation of the blue curve using transformations.
y=3^-x-2
500
$20,000 was put in an account with 4.5% interest compounded continuously. How much will be in the account after 18 years? Round to the nearest cent.
$44958.16