Algebra II Homework Week 13
Monday (11/26) –
1 𝑥
1. Graph 𝑦 = 3 (2) . Then state the domain and range.
2. Determine whether each function represents exponential growth or decay.
1 𝑥
b. 𝑦 = .4(7)𝑥
a. 𝑦 = 2 (6)
c. 𝑦 = 3.4(0.1)𝑥
3. Solve the equation 3𝑛−2 = 27
1 𝑦−3
4. Solve (7)
= 343
5. Solve 325𝑝+2 ≥ 16
6. Solve 49𝑥 = 7𝑥
2 −15
Tuesday (11/27) –
1. Write each equation in logarithmic form
a. 83 = 512
b. 5−3 =
1
1
125
c.1002 = 10
2. Write each equation in exponential form.
a. log 5 125 = 3
b. log13 169 = 2
2
c. log 8 4 = 3
3. Evaluate each expression.
a. log 2 16
1
c. log 5 57
b. log 2 32
4. Solve each equation or inequality.
a. log 9 𝑥 = 2
1
b. log 64 𝑦 ≤ 2
c. log 6 (2𝑥 − 3) = log 6 (𝑥 + 2)
Wednesday (11/28) –
1. Use a calculator to evaluate each expression to four decimal places.
a. a. log 19
b. log 0.75
2. EARTHQUAKES In 1906, San Francisco experienced a major earthquake of magnitude 8.3. In
1989, another major quake hit the area with a magnitude of 7.1. The amount of energy E, in ergs,
an earthquake releases is related to its Richter scale magnitude M by the equation log E = 11.8 +
1.5M. How much more energy did the 1906 quake release than the 1989 quake?
3. Solve 2a + 3 = 34.
4. Solve 5b – 1 ≥ 106 – b.
Algebra II Homework Week 13
5. Express log7 58 in terms of common logarithms. Then approximate its value to four decimal
places.
Thursday (11/29) –
1. Use a calculator to evaluate each expression to four decimal places.
a. e2.5
b. e–4.6
2. Use a calculator to evaluate each expression to four decimal places.
a. ln 15
b. ln 0.75
3. Write an equivalent exponential or logarithmic equation.
a. e–x = 2
b. ln e2a – 5
4. Solve –2e5x + 10 = 6.
5. Solve 6e–x < 15.
6. Solve each equation or inequality.
a. ln (6x – 3) + 3 = 10
b. ln (3x + 2) < 5
Friday (11/30) –
1. RECREATION A particular chemical must be added to a swimming pool at regular intervals
because it is released from the water into the air at the rate of 5% per hour. Sixteen ounces of the
chemical is added at 8 am. At what time will three–fourths of this chemical be gone from the
pool?
2. Exponential Decay of the Form y = ae–kt. CHEMISTRY The half–life of a radioactive
substance is the time it takes for half of the atoms of the substance to decay. Each element has a
unique half–life. Radon–222 has a half–life of about 3.8 days, while thorium–234 has a half–life
of about 24 days. Find the value of k for each element and compare their equations for decay.
3. In 1980, the value of farming land in a region of Wyoming was $150 per acre. Since then, the
value has increased by exactly 0.75% per year. If the land continues to increase in value at this
rate, what will the approximate value of the land per acre be in 2005?
A. $610
B. $330
C. $181
D. $175
E. $1098
kt
4. Exponential Growth of the Form y = ae . SAVINGS Sue invests $1000 at 5% interest
compounded continuously and Norma invests $1250 at 3.5% interest compounded continuously.
When interest is compounded continuously, the amount A in an account after t years is found
using the formula A = Pert, where P is the amount of principal and r is the annual interest rate. In
how many years will Sue’s account be greater than Norma’s account?