Exponential and Log Functions

Exponential Functions

100

Is 2*(0.99)^x an exponential growth or decay?

decay

200

What is the asymptote of f(x)=2^x? 

Make sure to include x= or y=

y=0

300

Convert the equation into log form:

9^1/2=3

log₉(3)=1/2

400

Solve 8^x=24

x=1.528

500

Solve 2*6^x=18. Round to the nearest thousandths.

x=1.226

Logarithmic Functions

100

Evaluate log2(7) to the nearest thousandths.

2.807

200

What is the x-intercept of ln(x)?

(1,0)

300

Solve log₅(125)=x

x=3

400

Solve log₂x=8

x=256

500

Solve 2log(x-3)=4

x=103

Applications

100

In the logistics growth problem below, what is the carrying capacity?

P(t)=230/(1+56.5e^-0.37t)

230

200

A colony of bacteria grows according to the function 

N(t)=100e^0.045t. What is the population after 5 days to the nearest tenth?

125.2 grams

300

Using A=Pe^rt, how much money will Susan have if she invests $1000 at an annual rate of 10% compounded continuously after 1 year?

$1105.17

400

A culture of 100 bacteria is put into a petri dish and the culture increases at a rate of 75% every hour. How much bacteria will be in the dish after 5 hours? Round to the nearest whole number.

1641 bacteria

500

Suppose the half-life of a certain radioactive substance is 40 days and there are 8 grams present initially. How much of the substance will be left after 120 days?

1 gram

Inverses & Properties

100

What is the base of log(15)?

10

200

Expand the following: 

log(2x³/y)

log2+3logx-logy

300

Condense the following:

2logx+3(logx-logy)

log(x⁵/y³)

400

Find the inverse of the following:

f(x)=2e^x+4-6

f^-1(x)=ln((x+6)/2)-4

500

Condense the following:

1/2[log₅(_x⁶)+log₅(x³)]

log₅(x^9/2)