Chapter 6 Review: Exponential and Logarithmic Functions

Flashcards for Chapter 6 Review: Exponential and Logarithmic Functions

Change log_m a = p to exponential form

m^p = a

Change c = e^d to logarithmic form

log_e c = d

Evaluate log_5 70

Approximately 2.640

The population of Axtonia is growing at a rate of 2.3% per year from a starting population of 57,768. If this rate continues, what will be the population in 10 years?

Approximately 72,518

What is the value of ln e^14?

14

Is the sequence 27, 9, 3, 1, 1/3, 1/9… geometric? If so, give the ratio.

Yes, the ratio is 1/3.

Write the explicit formula for the geometric sequence 8, 4, 2, 1,…Then, find the 8th term.

a_n = 8 * (1/2)^(n-1); 8th term = 0.0625

Write the explicit formula for the geometric sequence defined by the recursive formula: a1 = 8, an = 5 * a_(n-1) for n >= 2

a_n = 8 * (5)^(n-1)

Evaluate log_2 16

4

What will your balance be if you put $4,000 in your account and earn 5% interest compounded monthly for six years?

Approximately $5,796.07

You invest $25,000 and you earn 4% annual interest compounded continuously. How much money will you have in your account after five years?

Approximately $30,536.07

Write an example of an equation that models exponential decay. How do you know it represents exponential decay?

y = 2(1/2)^x because b = 1/2, which is between 0 and 1.

Solve: log3 4x + log3 2 = 3

x = 3.375

Expand: log (11/x^3)

log 11 - log x^3 = log 11 - 3log x

Write as a single log: log3 7 + log3 a

log_3(7a)

Use the Change of Base Theorem to rewrite log_3 5 as the quotient of two logarithms

log 5 / log 3

Solve: 3.4e^(2-2n) - 9 = -4

n ≈ 0.264

Solve: 2e^(3x-1) = 14

x ≈ 0.982

Earthquake intensity is measured by the Richter scale. If the intensity I = 989*I_0, what was likely the event?

Likely an earthquake, approximately R=3

Solve: 9^(n+10) + 3 = 81

n ≈ -8.017

Solve: log(3x + 1) = 2

x = 33

Expand the logarithm: log (3 * 2^3)

log 3 + 3log 2

Expand the logarithm: log (11x)^5

5log 11 + 5log x

Write as a single logarithm: 20log6 u + 5log6 v

log_6 (u^20 * v^5)

Find the sum of the series Σ(4^(k-1)) from k=1 to 7

5461

How many terms are in the geometric series 6, 18, 54, …, 3188646?

13

Graph y = 3(0.5)^x, then give the domain and range.

D: all real numbers, R: y > 0

Graph y = log(x+3) + 2, then give the domain and range.

D: x > -3, R: all real numbers