Q: If the demand function is $$p = 4000 - 10x$$ and $$x = 40$$, what is the total revenue $$R(x)$$?

$$R(40) = (4000 - 10 \times 40) \times 40 = 2400 \times 40 = 96000$$

Question 1

Which of the following is the correct solution to the exponential equation $$5^{2x-1} = 125$?

Accepted Answer

$$x = 2$$

Question 2

Given the equation $$3^{x^2-2x}$$ = \frac{1}{3}$$, what is the value of x$?

Accepted Answer

$$x = 1$$

Question 3

Solve for $$x$$: $$e^{x^2-x}$$ = $$e^6$$

Accepted Answer

$$x = 3 or$$ $$x = -2$$

Question 4

What is the exact solution to $$3^{x+2} = 7$?

Accepted Answer

$$x = \frac{\log 7}{\log 3} - 2$$

Question 5

If $$e^x = 3$$, what is the value of $$x to $$four decimal places?

Accepted Answer

$$x = \ln 3 \approx 1.0986$$

Question 6

Which property of logarithms allows you to write $$\log_b(MN) = \log_b M + \log_b N$$?

Accepted Answer

Product Rule

Question 7

Convert the logarithmic equation $$\log_5$ 25 = 2 to $$its equivalent exponential form.

Accepted Answer

$$25 = 5^2$

Question 8

What is the domain of the function $$f(x) = \ln(4 - x^2$)$$?

Accepted Answer

$$|x| \u003c 2$$

Question 9

Solve for $$x$$: $$\log_2$(x) + \log_2$(x-2) = 3$$

Accepted Answer

$$x = 4$$

Question 10

A population grows exponentially at a rate of 15% per year. How long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.15} \approx 4.62$$ years

Question 11

If $$p = 3000e$$^{-0.05x}$$ is the demand function and the price is p = 149.40$, how many units x$ are demanded (to the nearest unit)?

Accepted Answer

$$x = 60$$

Question 12

Given the compound interest formula $$A = P(1 + r)^t$$, how long will it take for $$1000 to $$grow to $$3000 at$$ $$12.5\%$$ compounded annually?

Accepted Answer

$$t = \frac{\ln 3}{\ln 1.125} \approx 9.69$$ years

Question 13

Which of the following is the correct application of the Power Rule for logarithms?

Accepted Answer

$$\log_b(M^p) = p \log_b M$$

Question 14

If $$\log_{10} x = 2$$, what is the value of $$x$$?

Accepted Answer

$$x = 100$$

Question 15

Solve for $$x$$: $$\ln(x+2) + \ln x = \ln(x+12)$$

Accepted Answer

$$x = 3$$

Question 16

A concrete cures at a rate of $$6.5\%$$ per day. How many days will it take to reach a compressive strength of $$20$$ MPa if the maximum strength is $$30$$ MPa?

Accepted Answer

$$t = \frac{\ln(1/3)}{-0.065} \approx 16.9$$ days

Question 17

If $$\log_2$ x = -3$$, what is the value of $$x$$?

Accepted Answer

$$x = \frac{1}{8}$$

Question 18

Which of the following is the correct change of base formula for logarithms?

Accepted Answer

$$\log_b a = \frac{\log_k a}{\log_k b}$$

Question 19

If the demand function is $$p = 4000 - 10x$$ and $$x = 40$$, what is the total revenue $$R(x)$$?

Accepted Answer

$$R(40) = (4000 - 10 	imes 40) 	imes 40 = 2400 	imes 40 = 96000$$

QMS110 Lecture 9

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드