Exponential Applications and Review Period_Date__

ACC. MATH II ASE QUIZ with HINTs Name______

Exponential Applications and Review Period_____Date______

I. Simplify each of the following expressions completely:

-4 6 3- 33 0 3 (a b c) ( a bc ) HINT: Organize your 23x+ 2 3x + 2 3x + 2 3x HINT: First, find a work, step by step Greatest Common Factor 1.) -3 2.) x a( a-5 c3 ( b - 2 c)) 2

HINT: “It sure would be nice…” II. Show work to solve each of the following algebraically: to have a common, smaller, base

+ + - 3.) 1005 3x = 10(0.0001) 4.) 1281 3x= (0.25) 3x 1

III. Consider the graph of f(x)= - 4 5x+ 2 - 6 HINT: Be sure to know your vocabulary

5.) What is the domain? ______

6.) What is the range? ______

7.) Write the equation for the asymptote. ______

8.) Write the coordinates of the y -intercept. ______

9.) End behavior: As x  ∞, then f(x)  ______.

IV. The function f(t) = 112000.(0.94)t describes a population over time.

10.) What is the population at t = 0? ______

11.) Is the population growing or decaying? ______

12.) What is the rate of growth/decay? ______Continued on the back V. Show work to algebraically find the exponential equation that contains these points: HINT: Points must fit in 13.) (0, 3) and (3, 375) the equation f(x) = a.bx 14.) (2, 16) and (5, 4)

VI. After winning $15000 in the lottery, Annabelle was offered several different HINT: Know your formulas investment opportunities. Find the value of each one after the specified time. for interest: A=P(1+r/n)nt 15.) A 3-year Certificate of Deposit paying 2% interest compounded monthly. or A=Pert (compounded continuously)

16.) A 5-year bond paying 3.2% interest compounded annually.

17.) A 2-year stock option paying 2.9% interest compounded continuously.

VII. According to their census, the population of Canada in 2000 was 30.689 million, and in 2010 the population was 34.149 million.

18.) Write an exponential function for the population of Canada as a function of the number of years since 2000. (Use f(x) = a.bx.)

19.) According to your equation, what is the annual population growth rate?

20.) According to your function, what was the population in 2005?

21.) According to your function, in what year did the population reach 25 million?

VIII. The half-life of a particular radium isotope is 60 days. (This means HINT: Use the equation f(x) = a.b x, with b=1/2 that half of this isotope will still be radioactive after 60 days.)

22.) What percent of this isotope should remain radioactive after 300 days?

23.) Write an equation for the percent of this isotope that will remain radioactive after t days.