Exponential/Logarithmic Functions NB

Vocab

100

A function who’s value is a constant raised to the power of the argument. 

Exponential function

200

A linethat continually approaches a given curve but does not meet it at any finite distance. 

Asymptote 

300

A function is _______ if there are no gaps in the domain of the function 

Continuous 

400

A function that matches each output with one input. 

One-to-one function

500

A logarithm to the base 10 is a _______ logarithm

Common logarithm

Change Forms

100

Convert the exponential equation 57 = y⁴ into logarithmic form

log_y57=4

200

Convert the exponential equation 7⁴ = x into logarithmic form.

4 = log₇x

300

Convert log₅y = 86 to exponential form

y = 5⁸⁶

400

log₄16= 2

4²=16

500

67 = 3^x

log₃67 = x

Log Equations

100

log (4x-3) = log 19

11/2

200

log₆(x/2 - 4)= log₆25

58

300

log x + log (x + 4) = log 12

2

400

log 5 - log (2x - 1) = 1

3/4

500

log₅x + log₅(x + 24) = 2

1

Solve for X

100

4^x=256

x = 4

200

2^x=30

x = log₂30

300

x⁵⁼ 243

x = 3

400

log₉27=x

x = 1.5

500

3^2x-1 = 27

x = 2

Word Problems

100

A material decays at a rate of 0.58% per year. How much of 240 grams of the material will be left in 7 years?

9.7 grams

200

After 24 days, 2 milligrams of an original 128 milligram sample remain. What is the half-life of the sample?

4 days

300

A $1,000 deposit is made at a bank that pays 12% compounded annually. How much will you have in your account at the end of 10 years?

$3,105.85

400

Mary's health bond will be worth $5713.81 in six years. If the interest rate is 6% that is compounded quarterly then what is the present value of the bond?

$4,500

500

An $1,000 investment is made in a trust fund at an annual percentage rate of 12%, compounded monthly. How long will it take the investment to reach $2,000?

5 years and 10 months