Exponents and Logarithms

Rewrite Exp. or Log. Functions

100

log_1/2(256)=-8

(1/2)^-8=256

200

10^b=5

Log5=b

300

Log_wm=a

w^a=m

400

e^-3=1/20

ln(1/20)=-3

500

ln(x²-15x+56)=-17

e¹⁷=x²-15x+56

Compound Interest

100

You receive $5000 to invest in a bank account paying 4.5% interest compounded annually. If you leave the money in there for 15 years, how much will you have?

$9676.41

200

You receive $200 to invest in a bank account paying 12.1% interest compounded monthly. If you leave the money in there for 5 years, how much will you have?

$365.14

300

If you invest $50 in a bank account paying 12% interest compounded quarterly, how long does it take if you wish to have $200?

t = 11.72 years

400

If you invest $322 in a bank account paying 2.2% interest compounded daily, how long does it take if you wish to have $400?

t= 9.86 years

500

How much will you have at the end of 5 years if you leave $610 in an account with 8.4% interest compounded continuously?

$928.40

Growth or Decay (and Why?)

100

y=3(2)^x

Growth, b>1

200

y=0.5(4)^x

Growth, b>1

300

y=6(1/2)^x

Decay, b<1

400

y=3(1)^x

Neither b=1

500

y=3(e)^-x

Decay, x is negative

Transformations And Functions

100

Write the Transformations

OG: y=3(2)^x

NEW: y= -(3/4)(2)^x-4 + 1

Reflection over the x-axis, vertical shrink by 1/4, vertical translation 1 up, horizontal translation 4 to the right

200

Write the Transformations

OG: y= log(x)+2

NEW: y= log(-2x) +4

Reflection over the y-axis, horizontal shrink by 1/2, vertical translation up 2 units

300

Write the function with the given transformations: 

OG: y=2^x

Translate 4 units up, 3 units to the right, vertical stretch by 9

y= 9(2)^x-3+4

400

Write the function with the given transformations: 

OG: y=log₅(x)

Translate 5 units to the left, Translate 3 units down, Vertical shrink by 1/3, Reflection over the x-axis

y= -(1/3)log₅(x+5) - 3

500

Write an exponential function that goes through the points (1, 15) (2, 45). 

y= 5(3)^x

Solve it! (log solutions as log or ln only)

100

Solve 2^x = 3

x=log₂3

200

2^x=4^x-1

x=2

300

log(x²+1)-log2=log13

x= 5, -5

400

log₃81²

8

500

log₂(x-1)+log₂x=1

x=2

Properties of Logarithms!

100

Condense: log4 + logx - logz

log(4x/z)

200

Expand: log₉(2x²/y⁸)

log₉2 + 2log₉x - 8log₉y

300

Condense:

2lny + ln(x³/2) - lnz

ln(y²x³/2z)

400

Expand: log₁₆₆(11*10³/7z⁵)

log₁₆₆11 + 3log₁₆₆10 - log₁₆₆7 - 5log₁₆₆z

OR  log₁₆₆11 + 3log₁₆₆10 -(log₁₆₆7 + 5log₁₆₆z)

500

Condense: log₂x + log₅y - 2log₂z + log₅k

log₂(x/z²) + log₅(ky)