Algebra 2 Exponential and Logarithmic Quiz Review

Basic Exponential Functions

100

What is the y-intercept of the following exponential function?

`f(x)=5(2)^x`

(0, 5)

200

Does the exponential function below show exponential growth or decay?

`f(x)=1/2(5)^x`

Exponential Growth

300

What is the y-intercept of the following exponential function?

`f(x)=-(1/2)^x`

(0, -1)

400

Does the exponential function below show exponential growth or decay?

`f(x)=4(2/3)^x`

Exponential Decay

500

What is the asymptote of the following exponential function.

`f(x)=2(3)^(x-5)+8`

y=8

Exponential Growth/Decay Word Problems

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

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

300

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

400

A bank account starts with $425 and earns 6.25% interest annually. How long will it take for there to be $dollars in the account, assuming no transactions have occured.

14.11 years.

500

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

Graphs of Exponential Functions

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

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 by a factor of 2.

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 by a factor of 3, shifted 4 units right, and shifted 5 units up.

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`

Check students' graph.

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`

Check students' graphs.

Common Logarithm

100

Without a calculator, evaluate the following logarithm.

log100

2

200

Without a calculator, evaluate the following logarithm.

`log (1/1000)`

-3

300

Write the exponential statement that corresponds to the logarithmic statement below.

`log1=0`

`10^0=1`

400

Write the exponential statement that corresponds to the logarithmic statement below.

`log10000=4`

`10^4=10000`

500

Write the logarithmic statement that corresponds to the exponential statement below.

`10^-3=1/1000`

`log(1/1000)=-3`

Solving Exponential and Logarithmic Functions

100

Solve the following.

2log₄x=1

x=2

200

Solve the following.

6^x-1=6

x=2

300

Solve the following.

2+ log₃x=6

x=81

400

Solve the following.

5*5^2x-1=35

(log₅7-1)/2

500

Solve the following

`4+3log2((16/3x))=13`

`x=3/2`