1. Warmup
Solve: log 𝟐 𝒙≤−𝟐

2. 6-10 Using Logarithms to Solve Exponential Problems
Solve problems involving exponential decay and growth. Solve logistic problems

3. f(x) = aekt works either way - if k is positive it is growth, if k is negative it is decay.
Exponential Growth and Decay The exponential decay formulas are of the form y = a(1 − r)t, or y = ae–kt.
The exponential growth formulas are of the form y = a(1 + r)t, or y = aekt.

4. 4. The half-life of Rubidium-87 is about 48.8 billion years.
a. Determine the value of k in the equation of decay for Rubidium-87.
b. A specimen currently contains 50 milligrams of Rubidium-87. How long will it take the specimen to decay to only 18 milligrams of Rubidium-87?

5. c. How many milligrams of Rubidium-87 will be left after 800 million years?
d. How long will it take Rubidium-87 to decay to one-sixteenth its original amount?

6. 𝑓 𝑡 = 𝑐 1 + 𝑎 𝑒 −𝑏𝑡

8. 10. The population of the state of Oregon has grown from 3
10. The population of the state of Oregon has grown from 3.4 million in 2000 to 3.9 million in 2012.
a. Write an exponential growth equation of the form 𝑦=𝑎 𝑒 𝑘𝑡 for Oregon, where t is the number of years after 2000.
b. Use your equation to predict the population of Oregon in 2025.

9. c. According to the equation, when will Oregon reach 6 million people?