Mini Exam 4 — Timed Mini Exams

Questions in this quiz (10)

1. The function $$H$$ models a periodic phenomenon. The maximum value of $$H$$ is $$10$$, which occurs at $$t=0$$. The period of $$H$$ is $$8$$ hours. For $$0 ≤ t ≤ 16$$, which of the following could be an expression for $$H(t)$$?

   • $$5\sin\left(\frac{\pi}{4}t\right)+5$$
   • $$5\sin\left(\frac{\pi}{2}t\right)+5$$
   • $$5\cos\left(\frac{\pi}{4}t\right)+5$$
   • $$5\cos\left(\frac{\pi}{2}t\right)+5$$

2. A data set is modeled by $$k(t)=12·3^t$$. The data are plotted on a semi-log graph where the vertical axis is scaled using the natural logarithm. Which of the following describes the appearance of the data?

   • Linear with slope 3
   • Linear with slope ln 3
   • Exponential curve concave up
   • Exponential curve concave down

3. The location of a point is given by polar coordinates $$(-2, \frac{3π}{4})$$. Which of the following gives another representation of this point?

   • $$(2,\frac{7\pi}{4})$$
   • $$(2,\frac{3\pi}{4})$$
   • $$(2,\frac{\pi}{4})$$
   • $$(-2,\frac{7\pi}{4})$$

4. The table shows values of a function $$f$$. Which function type best models the data?

   • Linear
   • Exponential
   • Quadratic
   • Polynomial of degree greater than 2

5. The height of a buoy in the ocean is modeled by a sinusoidal function $$h(t)$$. The buoy reaches a maximum height of $$4$$ feet and a minimum height of $$-4$$ feet. The time between consecutive maximum heights is $$6$$ seconds. Which of the following could represent $$h(t)$$?

   • $$4\sin\left(\frac{\pi}{3}t\right)$$
   • $$4\sin\left(\frac{\pi}{6}t\right)$$
   • $$2\sin\left(\frac{\pi}{3}t\right)$$
   • $$4\cos\left(\frac{\pi}{6}t\right)+4$$

6. Which of the following is equivalent to the expression $$4\left(\cos^2\left(\frac{3\pi}{5}\right)-\sin^2\left(\frac{3\pi}{5}\right)\right)$$?

   • $$2\cos\left(\frac{6\pi}{5}\right)$$
   • $$4\cos\left(\frac{6\pi}{5}\right)$$
   • $$2\sin\left(\frac{6\pi}{5}\right)$$
   • $$4\sin\left(\frac{6\pi}{5}\right)$$

7. The population of a town is decreasing over time. The population is modeled by the exponential function $$P(t)=15000(0.85)^t$$, where $$t$$ is measured in years since 2025. A revised model is given by $$Q(t)=15000(1.1)(0.85)^t$$. Which of the following describes the relationship between model $$Q$$ and model $$P$$?

   • The growth factor is increased by a factor of 1.1.
   • The initial value is increased by a factor of 1.1.
   • The growth factor is decreased by a factor of 1.1.
   • The initial value is decreased by a factor of 1.1.

8. Consider a circle centered at the origin in the $$xy$$-plane. An angle of measure $$\frac{\pi}{3}$$ radians in standard position subtends an arc of length $$30$$ units. What is the radius of the circle?

   • $$10$$
   • $$30$$
   • $$\frac{30}{\pi}$$
   • $$\frac{90}{\pi}$$

9. The function $$g$$ is given by $$g(x)=\frac{2-\sin x}{\cos x}$$. On the interval $$[0,2\pi]$$, what are all zeros of $$g$$?

   • $$g$$ has no zeros on $$[0,2\pi]$$
   • $$x=\frac{\pi}{2},\frac{3\pi}{2}$$
   • $$x=\frac{\pi}{6},\frac{5\pi}{6}$$
   • $$x=\frac{\pi}{2}$$ only

10. The number of people waiting in line at a concert is modeled by the function $$b(t)=30\cos\left(\frac{\pi}{20}t\right)+35$$ for $$0\le t\le40$$. Based on the graph of the model, which of the following is true?

    • The number of people is never $$0$$ because the vertical shift is greater than the amplitude.
    • The number of people is never $$0$$ because the amplitude is greater than the vertical shift.
    • The number of people reaches $$0$$ because the vertical shift is greater than the amplitude.
    • The number of people reaches $$0$$ because the amplitude is greater than the vertical shift.