Test Review!!!!!

Exponential Growth and Decay

100

Given  y=6(0.91)^x, what is the rate of decay? Write your answer as a percent

9%

200

Given an exponential function of the form y=ab^(x) , what condition must b  meet for exponential growth?

 b > 1  

300

A $12,000 car depreciates nine percent each year. What is the value of the car after five and a half years? Round to the nearest hundredth.

$7143.46

400

Given  y= 500(1.04)^x  find the y-intercept. Write your answer as an ordered pair, e.g. (x,y).

(0,500)

500

A baseball card bought for $50 increases in value by three percent each year. Now, the card is worth $60 dollars. How many years have past? Round to the nearest hundredth

6.17 years

The Number "e" and Compound Interest

100

What is the value of e to five decimal places?

2.71828

200

Evaluate  e^-3  to four decimal places.

0.0498

300

If you invest $10,000 with an interest rate of five percent, compounded quarterly, how much money will you have after 5 years? Round to the nearest hundredth.

$12,820.37

400

If you invest $5675.45 at a rate of six and a half percent, compounded weekly, how much money will you have after 10 years? Round to the nearest hundreth.

$10,867.14

500

You invested $17,000, compounded continuously at a rate of seven percent. It is now worth $51,874.87. How many years did your initial investment take to reach $51,874.87? Round to the nearest hundreth.

15.94 years.

Logarithms

100

Write log₂(32)=5 as an exponential equation.

2⁵=32

200

Write  (1/2)^(-4)=16  as a logarithmic equation

 log_(1/2)16=-4 

300

Evaluate  log_2 64 .

6

400

Given  y=-ln(x) + 2 , find the value of  y when  x=e .

y=1

500

Evaluate  log_(3.1)90.23. Round to the nearest hundreth.

3.98

Properties of Logarithms

100

Expand  log(xy^2) 

 logx +2logy 

200

Condense  2loga + 1/2logb 

 loga^2b^(1/2) 

300

Evaluate  lne^5.896 .

5.896

400

Expand  logroot5(xyz) .

 logx/3+logy/3+logz/3 

500

Condense  2(log2x-logy)-(log3+2log5) 

log( \frac(4x^2)(75y^2))

Exponential and Logarithmic Equations

100

Solve  for  x .  

16^(3x)=8

(Hint a^(x)=a^(y) impliesx=y )

x=1/4

200

Solve for  x 

 6^(2x)=75 

 Round to four decimal places.

 x=1.2048 

300

Solve for x 

lnx-ln2=3 . 

Round to three decimal places.

x \approx 40.171

400

An initial investment of $350 dollars is worth $429.20 after six years of continuous compounding. Find the annual interest rate. Round to four decimal places and report your answer as a percent.

3.3998%

500

 Solve for  x .

 log x +log(x-3)=1 

x=5