Calculus
MAC 1147 TEST 3
lessons 5, 6, 7
1. f(x)= x3
– 4×2
– 7x +10 given x=1 is a zero of the function.
A. show synthetic division.
B. list the solutions
C. factor the polynomial
D. Graph the polynomial
2. Graph. State the multiplicity of each solution
A. f(x) = x2
(x – 3)
B. f(x) = x( x 1)2
(x+3)
3. Write a polynomial function with the given zeros x= 2, 5, – 3
4. Graph the following: list any VA, HA, Domain and range
A. y = ex +2
B. y = ln(4 – x)
C. y= (
1
2
)
𝑥
− 5
5. Evaluate log4 12
6. Convert to log form x
7 = 13
7. Expand
A. log x2 √𝑥 − 6
3
B. ln (𝑥+2)
4
√𝑥
2+4
8. Write as a single 4ln(x 8) – 2lnx
9. Solve. Must round to 3 decimal places
A. e
3x = 4
B. e
2x +4 e
x – 12 = 0
C. 8
x = 12
D. 6
x + 1 = 23x
E. log2 (x – 2) +log2 (x +4) = 2
F. ln 2x= 4
10. Suppose you invest $1500 at 8.5% rate for 5 years. Calculate the interest earned if
invested
A. semiannually
B. continuously
11. How long will it take for $45000 to grow to $78000 at 10% rate if invested
continuously
12. How long will it take to double a $4000 at 9.5% rate if compounded
continuously
semi annually
quarterly
13. You bought an equipment for $900 in 2016. It is worth $595 in 2019. Assuming
continuous exponential function,
A. find the depreciation rate
B. write a function in terms of years
C. find the value of the computer in 2024
14. How much should be invested to have $5000 in 3 years at 4.4 percent rate compounded
A. monthly
B. continuously
15. Suppose you buy a car in 2015 for $19500. If your car is worth 15250 in 2018, how long
will it take for your to reach half of its worth?
16. Half life of an alien element is 4200 years. If 45 g of the element is remaining after
16800 years, what was the original amount of the substance.
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