MS 101 Alg & Trig test one • 05 June 2015 • Name:

1. Write the function to predict the number of descendants in generation x for a family in which each and every child in every generation has four children.
2. Use a spreadsheet to make an xy scatter graph of the following bouncing ball data.
   

   Bounce number	Bounce height (cm)
   0	100
   1	80
   2	64
   3	51.2
   4	40.96
   5	32.768

   1. Add an EXPONENTIAL trend line and equation to the graph. Write the exponential equation below:
   2. __________ Based on the exponential equation in part a, what will be the height of bounce number eight?
3. __________ A ball bounce function is given by f(x) = 100 × (0.80)ⁿ where n is the bounce number and f(x) is the bounce height. Calculate the height of the fifth bounce by evaluating this function at n = 5.
4. Circle the exponential equation: $y=8x$ | $y=8^x$ | $y=x^8$
5. __________ Evaluate $8^x$ for x = 0
6. __________ Evaluate $8^x$ for x = 3
7. __________ Evaluate $e^x$ for x = 3.8066625
8. __________ Evaluate log₁₀(x) for x = 10,000
9. __________ Evaluate log₁₀(x) for x = 500
10. __________ Evaluate ln_e(x) for x = 2.71828
11. __________ Evaluate ln_e(x) for x = 0
12. __________ Determine the value of x by rewriting as an exponential function: log₇(343) = x.
13. Sketch a graph of $y=2^{\left(\mathrm{–x}\right)}$ for x = -3 to 3
    
14. Use a spreadsheet to make an xy scatter graph of the following baby growth data.
    

    age in months post-conception	weight (pounds)
    9	7.17
    15	12.79
    21	16.49
    27	19.25
    33	21.47
    39	23.30

    1. Add a LOGARITHMIC trend line and equation to the graph. Write the logarithmic equation below:
    2. ____________ Based on the logarithmic equation in part a, calculate the weight of the baby at 45 months post-conception.
    3. ____________ Based on the logarithmic equation in part a, calculate the age in months post-conception when the weight will be equal to 25 pounds.
    4. Mathematically, why cannot the baby be started at an age of zero months?
       
       
15. Is log₀(0) a defined value? Why or why not?