MS 101 Alg & Trig test one 08 June 2012 Name:

1. __________ How many great-great... great-grandparents did you have in generation 12? That is, with you as generation zero, how many grandparents in the 12th generation?
2. __________ If one generation is 28 years, how many years ago would 12 generations be?
3. f(x) = __________ Suppose you have six children and they each have six children who each have six children and so forth. Write the function for this system. Use the variable x for the number of children.
4. __________ Use the above function for six children in every generation and WolframAlpha.com to determine the number of children in generation 4.
5. __________ The compound interest formula is given by:
   $A=P{(1+\frac{r}{n})}^{nt}$
   For a principal P of $1000, an interest rate r of 0.05, compounded n = 4 times a year, calculate the Amount A after a time t of ten years.
6. __________ The continously compounding interest formula is given by:
   $A=P{e}^{rt}$
   For a principal P of $1000, an interest rate r of 0.05,calculate the Amount A after a time t of ten years.
7. __________ Evaluate f(x) = log₁₀(x) for x = 1000.
8. __________ Evaluate f(x) = ln_e(x) for x = e.
9. __________ Marble bounce heights are described by the function:
   $f\left(x\right)=100e^{-0.65x}$ where x is the bounce number and f(x) is the bounce height. Evaluate this function at x = 10 bounces.
10. __________ Marble bounce heights are described by the function:
    $f\left(x\right)=100e^{-0.65x}$ where x is the bounce number and f(x) is the bounce height. Solve for the bounce number x where f(x) is two centimeters high .
11. Baby growth curves!
    
    The chart above depicts the theoretic optimal baby weight growth rate for three babies:
    
    My son: f(x) = 14.3 ln(x) - 24.9
    Baby MP: f(x) = 16.1 ln(x) - 27.5
    A healthy Vietnamese baby: f(x) = 12.3 ln(x) - 21.6.
    
    The x-axis is the age of the baby in months post conception. Birth is at x = 9 months. The y-axis is the weight of the baby in pounds.
    
    __________ Calculate the birth weight of baby MP by evaluating baby MP's growth function at x = 9 months.
12. __________ Calculate the weight of a Vietnamese baby at x = 24 months.
13. __________ Calculate the age of baby MP when baby MP's weight was equal to 22 pounds.
14. ____________ Evaluate the baby growth function 16.1 ln(x) - 27.5 at x = 480 months (that is 40 years old).
15. ____________ Is the result of the function a realistic weight in pounds for a 40 year old adult?