<p> ACC. MATH II ASE QUIZ with HINTs Name______</p><p>Exponential Applications and Review Period_____Date______</p><p>I. Simplify each of the following expressions completely:</p><p>-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</p><p>HINT: “It sure would be nice…” II. Show work to solve each of the following algebraically: to have a common, smaller, base</p><p>+ + - 3.) 1005 3x = 10(0.0001) 4.) 1281 3x= (0.25) 3x 1</p><p>III. Consider the graph of f(x)= - 4 5x+ 2 - 6 HINT: Be sure to know your vocabulary</p><p>5.) What is the domain? ______</p><p>6.) What is the range? ______</p><p>7.) Write the equation for the asymptote. ______</p><p>8.) Write the coordinates of the y -intercept. ______</p><p>9.) End behavior: As x  ∞, then f(x)  ______.</p><p>IV. The function f(t) = 112000.(0.94)t describes a population over time.</p><p>10.) What is the population at t = 0? ______</p><p>11.) Is the population growing or decaying? ______</p><p>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)</p><p>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)</p><p>16.) A 5-year bond paying 3.2% interest compounded annually.</p><p>17.) A 2-year stock option paying 2.9% interest compounded continuously.</p><p>VII. According to their census, the population of Canada in 2000 was 30.689 million, and in 2010 the population was 34.149 million. </p><p>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.)</p><p>19.) According to your equation, what is the annual population growth rate?</p><p>20.) According to your function, what was the population in 2005?</p><p>21.) According to your function, in what year did the population reach 25 million?</p><p>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.)</p><p>22.) What percent of this isotope should remain radioactive after 300 days?</p><p>23.) Write an equation for the percent of this isotope that will remain radioactive after t days. </p>