Chapter 7 Review

Properties

100

What is 2^x = 3 in log form

log₂3=x

200

log_bmⁿ= nlog_bm

The power property of logarithms 

300

Condense and simplify: 

2logx-logx+log3

log3x

400

list all transformations of the following exponential function: 

y=-2(1/4)^x+1+7

Scale factor of 2 

flipped over x axis

exp. decay

left 1

up 7

500

In the function A(t)=P(1+r/m)^mt m stands for?

the number of times your interest rate is compounded per year.

Solving Logs

100

log2x=1

x=5

200

2logx=-1

+/- (1/10)^1/2  

+/- sqrt(1/10)

300

2log(x+1)=5

+/- sqrt(10⁵)-1 = x

^{10^5 = 100000}

 

400

log(5-2x)=0

x=2

500

log₂4-log₂x=3

x=1/2

Solving Exponentials

100

2^x=3

log₂3=x

x= 1.58

200

3^x-1=72

log₃72+1=x

x=4.89

300

e^x+3=14

ln(14)-3=x

x=-.36

400

7-2e^x/2=1

2ln(3)=x

2.197

500

2+4^3x-2=100

log₄98=3x-2

(log₄98+2)/3

x=1.066

Interest Problems

100

You invest $400 in an account with interest compounded annually at a rate of 5%. After 5 years, how much is your money worth? 

400(1.05)⁵ = 510.51

$510.51

200

What is Pe^rt=A(t)

What is the equation for continuously compounded interest. 

300

What is the 'm' stand for in the general formula for compound interest? 

number of times your interest is compounded per year. 

400

You invest $5,000 in an account that compounds interest monthly at a rate of 7%. How long until your principal doubles in value? 

10 years

500

With a rate of 6% compounded continuously, how long would it take for a principal to triple in value? 

e^.06t=3

about 19 years

Variety

100

What is the formula for intensity difference between earthquakes of magnitude M1 and M2

log I1/I2 = M1-M2

200

Which NCAA basketball team was the first one to ever win the NCAA mens tournament? (hint: this school also lost the first NCAA national championship in football to the team the beat in the basketball tournament)

Oregon Ducks 46 -33 Ohio State (1939) B-ball

Oregon Ducks 20-42 Ohio State (2015) Football

300

What the name of the number 'e' = 2.718

Euler's Number

400

What is Mr. Peyton-Levine's favorite digital number? 

8

500

What speed in Km/sec does a rocket have to reach to leave earth's gravitational field? 

7.7 km/sec