Warm Ups

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

Daily Homework Quiz

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.

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

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

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

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

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

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

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 5.0397. The solution set consists of all real numbers in the interval

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.

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 =.046. 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.

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!

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