MTH 112 Section 97
Chapter 4 Quiz 2

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Quiz # Chapter4 quiz2

1) Solve for x: 3^2x = 81.

  (a) x = 13.5     (b) x = 1/4          (c) x = 4        (d) x = 2         (e) None of these

2)   Solve for x: log_x 8 = -3.

  (a) 2 (b) 512   (c) 1/2     (d) -2       (e) None of these

3) Solve for x:      3^5x+1 = 5.

(a) 0.1022     (b) 0.0930 (c) 0.1333     (d) 0.2218      (e) None of these

4) Solve for t:        e^0.0097t = 12.

(a) 256.1759     (b) -1237.1134     (c) 16,778,844.47     (d) -2.5886       (e) None of these

5)   Solve for x: log x + log(x + 3) = 1.   Type answer here.

6)  Solve the logarithmic equation accurate to three decimal places.  Use the calculator to find intersection.

ln x + ln(x + 3) = 1      Type answer here

7)   To solve  the logarithmic equation algebraically, the next step after these two would be:

      log x + log(x -3) = 1

      log[x(x -3)] = 1

(a) x(x - 3)= 1       (b)  x( x - 3) = log1         (c)   x( x - 3) = 10      (d)   x( x - 3) = e

8)  If $3700 is invested at 11 1/2 % interest compounded continuously,

find the balance, B, in the account after 5 years.  A = P( e ^rt)

(a) $3918.99 (b) $20,754.65 (c) $6575.38    (d) $7376.75 (e) None of these

9) In the above problem , at 11 1/2% interest, how long would it take (in years to one decimal place) for the money to triple?  ie  to grow to $11,100?  Type answer in space provided.    Use the calculator or algebra to solve.

years.  

10)  Given

Year	use value	sales in thousands
1990	0	42
1991	1	47
1993	3	53
1995	5	59
1996	6	67

the following data for sales of a new product. Construct a exponential regression and predict sales in the year 1999

Sales are to the nearest thousand dollars $ .

  Given  the same company, but the number of employees working, predict the number of employees in 1999 by using a logarithmic regression

Year	use value	#employees
1991	1	230
1993	3	235
1995	5	240
1996	6	241
1997	7	242

11) The equation is (to the nearest tenths):

(a)  y = 229.5x + 6.3     (b) 229.4 +6.3x     (c) 229.4x + log(6.3)     (d) 229.4 + 6.3 ln x

12) The prediction for the  number of employees in 1999 is employees (rounded to the nearest whole employee)

13)  Which of the following graphs accurately portrays the logarithmic function  and the data set in problem number 12?

(a)   (b)

(c)        (d)

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