If a painting is purchased for $1,000 and it happens to double in value every year, how much will it be worth 5 years from now?

1^st Test 1031 Calculus

1. If a painting is purchased for $1,000 and it happens to double in value every year, how much will it be worth 5 years from now?
2. $5,000 b. $32,000 c. $16,000       d. $10,000

2. Which of these pairs of lines are parallel?
3. 5x – 2y = 9 and 11 = 6y – 15x b. 6x – 3y = 4 and 6y – 9x = 18
4. 6x – 3y = 7 and 6y – 3x = 9 d. 5x + 2y = 13 and 12 = 6y – 15x

3. A drug dissipates at a continuous rate 12% per hour. How long until a quarter of the drug is left.

a.) 8.25  hours         b. 14.75 hours    c. 12.95 hours     d. 11.55 hours

4. Which relative change is biggest?
5. from 20 to 25 b. from 20 to 30 c. from 25 to 30    d. from 100 to 140

5. $1,000 placed into an account grows at 12% compounded annually. Placed into a different account it grows at 12% compounded quarterly. After 20 years, how much more money would you earn in the second account?
6. 1,376.90 b. 1722.10   c. 994.60     d. none of these

6. A very hot cup of coffee is placed on the kitchen table. Its temperature T (vertical axis) is plotted against the time spent on the table, t (the horizontal axis). The graph of T vs. t is best described as being
7. concave up and increasing b. concave down and increasing
8. concave up and decreasing d. concave down and decreasing

7. Which statement is true about the line through (8, -5) and (-5, 21)?
8. m=2 b. m= -2 c. m=1/2    d= -1/2

8. What is the ARC (average rate of change) of 7x² – 5x over [1, 3]?
9. 0 < ARC < 20 b. 20 < ARC < 30       c.  ARC > 45     d.   < -20

9. Solve for x (approximately). 3*4^x = 27
10. 2.81 b. 1.58 c.  .36          d.  1.39

10. Only one decomposition is right.
11. y = 1/(x ³ + 5) y = 1/u u = x³ + 5
12. y = f(x) = (x ² + 3) ⁷ y = u ² + 3 u = x ^1/7
13. y = sin (lnx) y = ln u u = sinx
14. y = [ln(10^x)] ⁴ y = 10^u u = [ln(x)] ⁴

11. A particle moves s = s(t) meters in t seconds

t          0    3     6      9     12

s(t)        0    7    21     38    52

The average velocity in meters per second between t = 3 and t = 9 is

12. 12.66 b. 4.67 c. 31.00     d.  5.17

12. The graph of y = x ² is a standard parabola. Which of these is the graph of y = (x – 2) ² + 3 moved ..

a.) to the right by 2 and up by 3      b.) to the left by 2 and up by 3

1. to the right by 3 and down by 2 d. none of these

13. Money is growing continuously according to the exponential function M(t) = $3,500e ^.08t

When will it be worth $10,500?

8. 8.7 years b. 13.7 c. 11.9 years    d. 14.6 years

14. Only one of the following sentences about f(x) is true. Which one?

x          3          6           9          12

f(x)       9.2         5.6          2.0         -1.6

1. f(x) cannot be exponential or linear b. f is exponential with r = -.40
2. f(x) is linear with intercept = 12.8     d. f(x) is linear with intercept 3

15. The following function shows exponential growth of money in an account after t years. What is the annual rate?

t            0             1            2                3

f(t)         $850         $952       $1066.24        $1194.19

1. 8% b. 10% c. 12%             d. 14%

16. A lawn mower costs $1,200 but depreciates (goes down in value) $90 every year. What equation describes its worth after x years?
17. W = 1,200*90^x b. W = 1,200 – 90^x      c. W = 1,200 – 90x         d. 1,200 + (1 – .90)x

17. Radioactive Globarium lose 3% of its radioactivity annually. Which formula describes its radioactivity after t years?
18. G(t) = G₀ e^-03t b. G(t) = G₀ e^-.03t   c.  G(t) = G₀ e^.97t     d. G(t) = G₀ e^-.97t    

18. The function y = 2 sin 4x has amplitude and period equal to
19. 2, 4 b. 4, 2pi c. 2, pi/2   d. 2, 2pi

19. A drug dissipates at a continuous rate of 10% an hour. When will there be half of it left?
20. 3 hours b. 5 hours c 7 hours     d. 9 hours

20. What is the equation of the line with slope -4 and going through the point (2, 14)?
21. 2y – 4x = 14 b. y – 4x = 14 c. y + 4x = 22     d. =y = -4x + 14