Solve the exponent
Growth/Decay
Graphs
Let it roll (gently)
All about that base
100
What is the y-intercept of the following exponential function? HINT: when x = 0, y = ?
f(x)=5(2)^x
(0, 5)
5=5(2)^0
100
You deposit $1000 in a bank account that will earn simple interest of 4% per year. How much will your investment be worth after 8 years?
$1368.57
1368.57=1000(1+ (.04)^8
100
Describe the transformations that take place to get the graph of g(x) from the parent function f(x).
f(x)=3^x
g(x)=3^(x+2)-5
Shifted 2 units left and 5 units down
100
Without a calculator, evaluate the following logarithm.
log100
2
100
Use properties of logarithms to condense the following logarithmic expression into a single logarithm.
log5-log9
log(5/9)
200
What is f(2)?
f(x)=1/2(4)^x
f(2)=1/2(4)^2 = 8
200
The number of bacteria in a petri dish doubles every hour. If you start with 6 bacteria, how many will you have after 12 hours?
24,576 bacteria
Doubling = increasing by 100% or 1.00
24,576 = 6(1+1.00)^12
200
Describe the transformations that take place to get the graph of g(x) from the parent function f(x).
f(x)=e^x
g(x)=-2e^x
Reflected across the x-axis and vertically stretched (skinnier) by a factor of 2.
200
Without a calculator, evaluate the following logarithm.
log (1/1000)
-3
200
Use properties of logarithms to condense the following logarithmic expression into a single logarithm.
10log5+log8
log(5^10*8)
300
What is the value of x?
-8=-(1/2)^x
x = -3
-8=-(1/2)^-3
300
A car is purchased for 90,000 riyals (haha!). It is expected to lose 15% of its value each year. How much will the car be worth after 5 years?
1 riyal = $0.27
39,933.48 riyals or $10,782.03
39,933.48 = 90,000(1-.15)^5
300
Describe the transformations that take place to get the graph of g(x) from the parent function f(x).
f(x)=(1/2)^x
g(x)=-3(1/2)^(x-4)+5
Reflected across the x-axis, stretched (skinnier) by a factor of 3, shifted 4 units right, and shifted 5 units up.
300
Write the exponential statement that corresponds to the logarithmic statement below.
log1=0
10^0=1
300
Use properties of logarithms to expand the following logarithmic expression.
log(4^5*3)
5log4+log3
400
Does the exponential function below show exponential growth or decay?
f(x)=4(2/3)^x
Exponential Decay
400
A bank account starts with $425 and earns 6.25% interest monthly. How much money will be in the account in 15 years assuming no transactions have occured.
$1,082.63
1,082.63=425(1+(.0625/12))^(12x15)
400
Graphing! Graph the function g(x) and its parent function f(x) on the same coordinate plane.
f(x)=2^x
g(x)=2^(x+3)-5
Skinnier, left 3, down 5
400
Write the exponential statement that corresponds to the logarithmic statement below.
log10000=4
10^4=10000
400
Use properties of logarithms to expand the following logarithmic expression.
log(5/12)^3
3log5-3log12
500
What is the horizontal asymptote of the following exponential function.
f(x)=2(3)^(x-5)+8
y=8
500
The population of a town is decreasing at a rate of 5% per year. This year there are 10,000 people in this town, how many people will be left in 20 years from now? (round to the nearest whole number)
3,585 people
3,584.85 = 10,000(1-.05)^(20)
500
Graphing! Graph the function g(x) and its parent function f(x) on the same coordinate plane.
f(x)=e^x
g(x)=-1/2(e)^x+2
Flipped, fatter, left 2
500
Write the logarithmic statement that corresponds to the exponential statement below.
10^-3=1/1000
log(1/1000)=-3
500
Use properties of logarithms to condense/expand the following logarithmic expression.
log((9^3*6)/4^5)
3log9+log6-5log4