Exponentials and Logarithms Review!

Exponential Functions

100

What is the formula for Exponential Functions? How do you know if the function is growing or decaying? 

f(x) = a*b^x

If "b" is greater than 1, the function is growing

If "b" is less than 1, the function is decaying

200

Fidel has a rare coin worth $550. Each decade, the coin's value increases by 10%. What expression gives the coin's value, 6 decades from now?

550(1 + 0.1)⁶

300

Find the Exponential Function when given the points:
(1,3) and (2, 4.5)

f(x) = 2(1.5)^x

400

Find the Exponential Function when given the points: 

(2,2) and (3,4) 

f(x) = (1/2)2^x

500

Find the Exponential Function when given the values: 

f(-2)= 6.25 and f(2)= .01

f(x)= 1/4(.2)^x

Compounding Interest

100

What is the formula used when compounding interest? 

A = P(1 + r/n)^nt

200

What is the formula used when compounding interest continuously? 

A = Pe^rt

300

Becky invested $19,800 in a CD that pays an annual interest rate of 5.3%. The CD is set to compound daily. How much is in Becky’s account after 9 years?

$31,901.32

400

Jake invests in an annuity with an annual fixed interest rate of 6.2%. The annuity compounds monthly. If after 10 years, the account balance is $27,839.45, how much was the beginning investment?

$15,000

500

A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1,854.00, what will the balance be 5 years from now? 

1854e^{0.03 x 5} ≈ $2,154.04

Solving Exponentials

100

Solve:  

3^b= 17

*Remember, in order to solve a variable trapped in the exponent, you must use LOGS!

2.5789

200

Solve: 

5 ⋅ 18^6x = 26

0.0951

300

Solve: 

16^n-7+ 5 = 24

8.062

400

Re-write in Logarithmic Form

5 ⋅ 6^3m = 20

(log₆4) / 3 = m 

500

What is it called when algebraic processes give us a solution that is false? 

An Extraneous Solution

Expanding and Condensing Logarithms

100

Expand this Log: 

log(3x⁴y^-7)

log(3) + 4log(x) -7log(y)

200

Condense this Log: 

2log₄(x) + 5log₄(y) - 1/2log₄(z)

log₄(x²y⁵ / z^1/2) 

300

Expand this Log: 

ln(4x³/2y)

ln 4 + 3 ln x - ln 2 - ln y 

400

Condense this Log: 

ln 5 - 7 ln x⁴ + 2 ln y

ln (5y² / x²⁸) 

500

What is the name of the formula that allows us to evaluate a logarithm with any base? 

The Change of Base Formula

Solving Logarithmic Functions

100

Solve: 

log (5x) = log (2x + 9)

3

200

Solve: 

−2log₅ (7x) = 2

1/35

300

Solve: 

−6log₃ (x − 3) = −24

84

400

Solve: 

log₁₀ (2) + log₁₀ (x) = 1

5

500

Solve:

log₂ (2x) = log₂ (100)

50