Q: A savings account offers $$6\%$$ APR compounded quarterly. What is the annual percentage yield (APY)?

$$\text{APY} = (1 + \frac{0.06}{4})^4$ - 1 \approx 0.0614 or$$ $$6.14\%$$

Q: A $$1000$$ investment grows continuously at $$3\%$$ per year. What is its value after $$10$$ years?

$$A = 1000 \cdot e$$^{0.03 \times 10}$$ = 1000 \cdot e$$^{0.3}$$ \approx 1349.86$$

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 height of $$2$$ meters with an initial velocity of $$10 m/s. $$Its height after $$t$$ seconds is $$h(t) = -5t^2$ + 10t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$12$$ meters

Question 5

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 6

Given $$f(x) = 3x - 2$$, find the inverse function $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 2}{3}$$

Question 7

A savings account offers $$6\%$$ APR compounded quarterly. What is the annual percentage yield (APY)?

Accepted Answer

$$	ext{APY} = (1 + \frac{0.06}{4})^4$ - 1 \approx 0.0614 or$$ $$6.14\%$$

Question 8

Which of the following describes a function that is concave up and decreasing?

Accepted Answer

The graph bends upward like a cup, but the values decrease as $$x$$ increases.

Question 9

Given two points $$(0, 100)$$ and $$(3, 800)$$, find the exponential equation $$y = a b^t$$ passing through both points.

Accepted Answer

Question 10

A $$1000$$ investment grows continuously at $$3\%$$ per year. What is its value after $$10$$ years?

Accepted Answer

$$A = 1000 \cdot e$$^{0.03 	imes 10}$$ = 1000 \cdot e$$^{0.3}$$ \approx 1349.86$$

Question 11

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

Accepted Answer

$$x = 2$$

Question 12

A radioactive substance decays according to $$Q(t) = 500 e$$^{-0.05 t}$$. What is the continuous decay rate k$?

Accepted Answer

$$k = -0.05$$

Question 13

Which of the following is the horizontal asymptote for $$f(x) = 7 \cdot 0.5^x$$?

Accepted Answer

$$y = 0$$

Question 14

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

Question 15

If $$f(x) = x^2$ - 6x + 8$$, what are the zeros of the function?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 16

A medication decays exponentially in the bloodstream. If the amount halves every $$4$$ hours, what is the continuous decay rate $$k$$?

Accepted Answer

$$k = \frac{\ln(0.5)}{4} \approx -0.173$$

Question 17

If $$f(x) = 2x + 3$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(4) = 2 \cdot 4 + 3 = 11$$

Question 18

A population grows according to $$P(t) = 2000 e$$^{kt}$$ and doubles in 7$ years. What is the value of k$?

Accepted Answer

$$k = \frac{\ln(2)}{7} \approx 0.099$$

Question 19

Which transformation will shift the graph of $$f(x)$$ right by $$4$$ units and up by $$5$$ units?

Accepted Answer

$$g(x) = f(x - 4) + 5$$

Precalculus Study Guide: Functions, Quadratics, and Exponentials

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