Lesson 65 Solving Exponential Functions
Essential QuestionHow can you solve an exponential equation graphically?EXPLORATION 1Solving an Exponential Equation GraphicallyWork with a partner. Use a graphing calculator to solve the exponential equation 2.5x 3 = 6.25 graphically. Describe your process and explain how you determined the solution.
EXPLORATION 2The Number of Solutions of an Exponential EquationWork with a partner.a. Use a graphing calculator to graph the equation y = 2x.b. In the same viewing window, graph a linear equation that does not intersect the graph of y = 2x.c. In the same viewing window, graph a linear equation that intersects the graph of y = 2x in more than one point.d. Is it possible for an exponential equation to have no solution? more than one solution? Explain your reasoning.
EXPLORATION 3Work with a partner. Use a graphing calculator to solve each equation.a. 2x = \b. 2x + 1 = 0
Question 41.MODELING WITH MATHEMATICSYou scan a photo into a computer at four times its original size. You continue to increase its size repeatedly by 100% using the computer. The new size of the photo y in comparison to its original size after x enlargements on the computer is represented by y = 2x + 2. How many times must the photo be enlarged on the computer so the new photo is 32 times the original size?Answer:
In Exercises 4346, solve the equation.
Question 43.
Explain how you can use mental math to solve the equation 8x 4 = 1.Answer:
In Exercises 5358, solve the equation.
Question 53.
The Speed Of A Falling Object Can Be Modeled Using The Equation
.72 1
ts t e
, where t is the number
of seconds it has been falling and s is the speed in feet per second. Which of the following is closest to the
number of seconds it will take for the object to reach a speed of 60 feet per second?
4 5.
Answer Key – Unauthorized posting of key to any website is prohibited and a violation of copyright.
COMMON CORE ALGEBRA II, UNIT ASSESSMENTS UNIT #4 FORM B
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Posted on 26-Jan-2022
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Lesson 64 Exponential Growth And Decay
Essential QuestionWhat are some of the characteristics of exponential growth and exponential decay functions?
EXPLORATION 1Predicting a Future EventWork with a partner. It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. By the 1960s, this number had dropped to about 500 nesting pairs. In 1967, the bald eagle was declared an endangered species in the United States. With protection, the nesting pair population began to increase. Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species.Describe the pattern shown in the graph. Is it exponential growth? Assume the pattern continues. When will the population return to that of the late 1700s? Explain your reasoning.
EXPLORATION 2Describing a Decay PatternWork with a partner. A forensic pathologist was called to estimate the time of death of a person. At midnight, the body temperature was 80.5°F and the room temperature was a constant 60°F. One hour later, the body temperature was 78.5°F.a. By what percent did the difference between the body temperature and the room temperature drop during the hour?b. Assume that the original body temperature was 98.6°F. Use the percent decrease found in part to make a table showing the decreases in body temperature. Use the table to estimate the time of death.
Communicate Your Answer
What are some of the characteristics of exponential growth and exponential decay functions?
y = t + 2
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Lesson 61 Properties Of Exponents
Essential QuestionHow can you write general rules involving properties of exponents?
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Communicate Your Answer
How can you write general rules involving properties of exponents?
Question 3.There are 33 small cubes in the cube below. Write an expression for the number of small cubes in the large cube at the right.
6.1 Lesson
Question 14.)-2
Monitoring Progress
Question 15.Write two expressions that represent the area of a base of the cylinder in Example 5.
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