Basic Exponential Functions
What is the y-intercept of the following exponential function?
f(x)=5(2)^x
(0, 5)
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
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
Without a calculator, evaluate the following logarithm.
log100
Use properties of logarithms to condense the following logarithmic expression into a single logarithm.
log5-log9
log(5/9)
Does the exponential function below show exponential growth or decay?
f(x)=1/2(5)^x
Exponential Growth
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
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 by a factor of 2.
Without a calculator, evaluate the following logarithm.
log (1/1000)
-3
Use properties of logarithms to condense the following logarithmic expression into a single logarithm.
10log5+log8
log(5^10*8)
What is the y-intercept of the following exponential function?
f(x)=-(1/2)^x
(0, -1)
A car is purchased for 90,000 riyals. It is expected to lose 15% of its value each year. How much will the car be worth after 5 years?
39,933.48 riyals
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 by a factor of 3, shifted 4 units right, and shifted 5 units up.
Write the exponential statement that corresponds to the logarithmic statement below.
log1=0
10^0=1
Use properties of logarithms to expand the following logarithmic expression.
log(4^5*3)
5log4+log3
Does the exponential function below show exponential growth or decay?
f(x)=4(2/3)^x
Exponential Decay
A bank account starts with $425 and earns 6.25% interest annually. How much money will be in the account in 15 years assuming no transactions have occured.
$1055.17
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
Check students' graph.
Write the exponential statement that corresponds to the logarithmic statement below.
log10000=4
10^4=10000
Use properties of logarithms to expand the following logarithmic expression.
log(5/12)^3
3log5-3log12
What is the asymptote of the following exponential function.
f(x)=2(3)^(x-5)+8
y=8
A graphic artist starts with an image that is 10 inches long and 7 inches wide. He repeatedly scales the image to be 80% of the previous image's size. How big will the image be if he does this reduction 8 times. Round to two decimal places.
1.68 inches long by 1.17 inches wide
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
Check students' graphs.
Write the logarithmic statement that corresponds to the exponential statement below.
10^-3=1/1000
log(1/1000)=-3
Use properties of logarithms to condense/expand the following logarithmic expression.
log((9^3*6)/4^5)
3log9+log6-5log4