Question 1

Which of the following best describes the graph of an equation in two variables?

Accepted Answer

A drawing that represents all ordered pairs that are solutions of the equation.

Question 2

Given the equation $$2x + 1 = y$$ and $$125x^2 + 25 = y$, which of the following is a solution to both equations?

Accepted Answer

$$(1, 3) is a $$solution to $$2x + 1 = y$$ but not to $$125x^2 + 25 = y$.

Question 3

Suppose $$P = 1000 is $$invested at an annual interest rate of $$5\%$$, compounded annually. What is the amount $$A in $$the account at the end of 2 years? (Use $$A = P(1 + r)^t)$$

Accepted Answer

$$A = 1000(1 + 0.05)^2$ = 1102.50$$

Question 4

If $$P$$ dollars are invested at an interest rate $$r$$ compounded $$n$$ times per year for $$t$$ years, which formula gives the amount $$A in $$the account?

Accepted Answer

$$A = P \left(1 + \frac{r}{n}\$$right)^{nt}$$

Question 5

Jen invests $$2000 in the Green View Fund at 2.75$$\%$$ interest, compounded quarterly. How much is in the account at the end of 3 years? (Use A = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$)

Accepted Answer

$$A = 2000 \left(1 + \frac{0.0275}{4}\$$right)^{12}$$ \approx 2184.13$$

Question 6

Which of the following statements about mathematical models is correct?

Accepted Answer

Mathematical equations can serve as models in a wide variety of applications.

Question 7

A scientist is tracking the growth of a bacteria population, which doubles every hour. If the initial population is $$P_0$$, which equation models the population after $$t$$ hours?

Accepted Answer

$$P = P_0$ \cdot 2^t$$

Question 8

Which of the following is NOT a correct step in plotting the graph of an equation in two variables?

Accepted Answer

Listing all possible values of one variable only.

Question 9

A $$5000$$ investment grows to $$6100 in$$ $$4$$ years with interest compounded annually. What is the annual interest rate $$r$$? (Use $$A = P(1 + r)^t)$$

Accepted Answer

$$r = (\frac{6100}{5000}$$)^{1/4}$$ - 1 \approx 0.05$$

Question 10

Which of the following best explains why technology can be useful in graphing equations?

Accepted Answer

Technology can quickly plot points and reveal patterns that may not be easily seen by hand.

Question 11

A chemical reaction's concentration $$C$$ decreases by $$10\%$$ each hour. If the initial concentration is $$C_0$$, which equation models the concentration after $$t$$ hours?

Accepted Answer

$$C = C_0$ \cdot (0.9)^t$$

Question 12

If $$A = P(1 + r)^t$$ and $$A = 2000$$, $$P = 1500$$, $$t = 5$$, what is the annual interest rate $$r ($$rounded to the nearest percent)?

Accepted Answer

$$r = (\frac{2000}{1500}$$)^{1/5}$$ - 1 \approx 0.06$$

Question 13

Which of the following is a correct interpretation of the ordered pair $$(x, y) as a $$solution to an equation in two variables?

Accepted Answer

It means that substituting $$x$$ and $$y$$ into the equation makes the equation true.

Question 14

A $$1200$$ investment is compounded monthly at $$3\%$$ annual interest. What is the amount after $$2$$ years? (Use $$A = P \left(1 + \frac{r}{n}\$$right)^{nt}$$, n = 12$)

Accepted Answer

$$A = 1200 \left(1 + \frac{0.03}{12}\$$right)^{24}$$ \approx 1273.41$$

Question 15

Which of the following is a real-world application of graphing equations?

Accepted Answer

Predicting the future value of an investment using compound interest.

Question 16

If $$A = P \left(1 + \frac{r}{n}\$$right)^{nt}$$, what does the variable n$ represent?

Accepted Answer

The number of times interest is compounded per year.

Graphs of Equations and Compound Interest: Foundations for Calculus

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