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Chapter 5: Q. 78 (page 284)

Solve given equation and verify your result using graphing utility.

e3x=e2-x

Short Answer

Expert verified

The solution set is{12}and it is verified through graph.

Step by step solution

01

Step 1. Given information

The given equation is :

e3x=e2-x

We have to solve for x and verify using graphing utility.

02

Step 2. Comparing the expressions having same bases and solving for x .

Since bases are same , therefore the exponential powers should also be the same.

3x=2-x3x+x=24x=2x=24x=12

03

Step 3. Verification using graphing utility

Graph

Y1=e3xY2=e2-x

Determine the point of intersection.

The graph intersects at x=12.

So the solution set is{12}.

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Most popular questions from this chapter

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False

To graph (x-2)3, shift the graph of y=x3to the left 2 units.

Vehicle Stopping Distance Taking into account reaction time, the distance d(in feet) that a car requires to come to a complete stop while traveling rmiles per hour is given by the function

localid="1646198784356" d(r)=6.97r-90.39

a. Express the speed rat which the car is traveling as a function of the distance localid="1646198792401" drequired to come to a complete stop

b. Verify that localid="1646198797631" r=r(d)is the inverse of localid="1646198802104" d=d(r)by showing that localid="1646198806352" r(d(r))=rand localid="1646198811055" d(r(d))=d

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" 300feet.

d(r(d))=d

If 2x=3, what does4-xequal?

solve each equation. Verify your results using a graphing utility.

9-x+15=27x

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

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