1. Warm Ups

2. Solving Exponential and Logarithmic Inequalities
Lesson 4.8
Unit 4b Day 2
Essential Question:
How do we solve exponential and logarithmic inequalities?
Sunday, July 07, 2019

3. Daily Homework Quiz

4. Vocabulary
An exponential inequality in one variable can be written in the form.
An logarithmic inequality in one variable can be written in the form.
Inequalities can be used to describe subsets of real numbers called intervals.

5. Key Concept
Exponential and logarithmic inequalities can be solved graphically or by using the table feature on a graphing calculator.

6. GUIDED PRACTICE
Tell whether the given x-value is a solution of the
inequality.
Yes
Yes
Yes

7. GUIDED PRACTICE
Complete the table. Use the table to solve the inequality. x
0.5 1
1.5 2
2.5 5x

8. GUIDED PRACTICE
Complete the table. Use the table to solve the inequality. x
.25
0.5
0.75 1
1.25
1.5
log4x

9. Solve an exponential equation using technology
EXAMPLE 1
Solve an exponential equation using technology
Write the inequality in standard form and as a function.
The critical x-value is 1.5
The solution set consists of all real numbers in the interval

10. Solve a logarithmic equation using technology
EXAMPLE 2
Solve a logarithmic equation using technology
Write the inequality in standard form and as a function.
The critical x-value is 9, but logarithms have a vertical asymptote.
The solution set consists of all real numbers in the interval

11. Solve a logarithmic equation using technology
GUIDED PRACTICE
Solve a logarithmic equation using technology
Write the inequality in standard form and as a function.
The critical x-value is
The solution set consists of all real numbers in the interval

12. Solve a logarithmic equation using technology
GUIDED PRACTICE
Solve a logarithmic equation using technology
Car Value Your family purchases a new car for $25,000. It value depreciates by 12% each year. During what interval of time does the car’s value exceed $16,000.
So, the car’s value exceeds $16,000 for about the first 3 and a half years after it is purchased.

13. Newton’s Law of Cooling
The temperature T of a cooling substance at time t (in minutes) is:
T = (T0 – TR) e-rt + TR
T0= initial temperature
TR= room temperature
r = constant cooling rate of the substance
Cooking Stew You’re cooking stew. When you take it off the stove the temp. is 212°F. The room temp. is 70°F and the cooling rate of the stew is r = You want to eat the soup when the temperature is between 130°F and 140°F. Write an inequality that gives the time interval in which this would occur.

14. T0 = 212, TR = 70, r = .046 T = (T0 – TR) e-rt + TR
T = (212 – 70) e-0.46t + 70
You should serve your soup between 15 and 19 minutes after you take it off the stove!

15. Assignment: Class work: Practice Worksheet 4.8
Homework: Page 167 # 1 – 20.