Q: A savings account offers $$3\%$$ APR compounded quarterly. What is the annual percentage yield (APY)?

$$\text{APY} = (1 + \frac{0.03}{4})^4$ - 1 \approx 0.0304$$

Q: A $$1200$$ investment earns $$6\%$$ APR compounded monthly for $$4$$ years. What is the final amount?

$$A = 1200\left(1 + \frac{0.06}{12}\$$right)^{12 \times 4}$$ \approx 1520.60$$

Q: A rectangular field is to be fenced along three sides (the fourth side borders a river) with $$120$$ meters of fencing. What is the maximum area that can be enclosed?

$$A_{\text{max}} = 1200$$ square meters

Question 1

A hospital records the number of bacteria in a sample as $$N(t) = 500 \cdot 1.08^t$$, where $$t is $$measured in hours. What is the percentage growth rate per hour?

Accepted Answer

$$8\%$$

Question 2

A function $$f(x)$$ has a point $$(2, 5). $$What is the corresponding point on $$g(x) = f(x + 3) - 4$$?

Accepted Answer

$$(5, 1)$$

Question 3

Which of the following functions passes the Horizontal Line Test and therefore has an inverse?

Accepted Answer

$$f(x) = 2x + 1$$

Question 4

A ball is thrown upward from a bridge. Its height (in feet) after $$t$$ seconds is $$h(t) = -16t^2$ + 32t + 80. $$What is the maximum height reached by the ball?

Accepted Answer

$$112$$ feet

Question 5

Which equation models continuous exponential decay with a rate $$k = -0.07$$ and initial amount $$a = 200$$?

Accepted Answer

$$Q(t) = 200 e$$^{-0.07t}$$

Question 6

A savings account offers $$3\%$$ APR compounded quarterly. What is the annual percentage yield (APY)?

Accepted Answer

$$	ext{APY} = (1 + \frac{0.03}{4})^4$ - 1 \approx 0.0304$$

Question 7

Given $$f(x) = 2x - 5$$, what is the formula for $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{2}$$

Question 8

A population doubles every 6 years. What is the continuous growth rate $$k$$?

Accepted Answer

$$k = \frac{\ln(2)}{6}$$

Question 9

Which statement best describes the difference between linear and exponential models?

Accepted Answer

Linear models change by a constant absolute amount; exponential models change by a constant percentage.

Question 10

A function $$f(x) is $$concave up and decreasing. Which sketch best represents its graph?

Accepted Answer

A curve bending upward (like a cup) but sloping down as $$x$$ increases.

Question 11

Given two points $$(0, 100)$$ and $$(3, 800)$$, what is the exponential equation $$y = a b^t$$ passing through them?

Accepted Answer

$$y = 100 \cdot 2^t$$

Question 12

A $$1200$$ investment earns $$6\%$$ APR compounded monthly for $$4$$ years. What is the final amount?

Accepted Answer

$$A = 1200\left(1 + \frac{0.06}{12}\$$right)^{12 	imes 4}$$ \approx 1520.60$$

Question 13

If $$f(x) = x^2$ - 4x + 7$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 2$$

Question 14

Which of the following is the correct composition $$(f \circ g)(x) if$$ $$f(x) = x^2$ and g(x) = 3x + 1$?

Accepted Answer

$$(f \circ g)(x) = (3x + 1)^2$

Question 15

A radioactive substance decays continuously at rate $$k = -0.05. $$What is the half-life?

Accepted Answer

$$t_{1/2} = \frac{\ln(2)}{0.05}$$

Question 16

Which transformation will shift the graph of $$f(x)$$ right by $$4$$ units and up by $$7$$ units?

Accepted Answer

$$g(x) = f(x - 4) + 7$$

Question 17

A function $$Q(t) = 500 \cdot 0.9^t$$ models the amount of medicine in the bloodstream. What is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 18

If $$b = 1.05$$, what is the equivalent continuous growth rate $$k$$?

Accepted Answer

$$k = \ln(1.05)$$

Question 19

A rectangular field is to be fenced along three sides (the fourth side borders a river) with $$120$$ meters of fencing. What is the maximum area that can be enclosed?

Accepted Answer

$$A_{	ext{max}} = 1200$$ square meters

Precalculus Study Guide: Functions, Quadratics, and Exponential Models

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