3 Find a formula for the exponential function passing through the points (-2, 4) and (1,6) y = The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced to a mass of 1 mg. What was the initial mass (in mg) of the sample? What is the mass 8 weeks after the start? B K R Match each equation with a graph above 4(1.27)* 3(0.83) 3(0.74)* a. green (G) b. red (R) c. black (K) | 3(1.27) d. blue (B) | 3(1.56) e. orange (O) Write an equation for the transformed logarithm shown below, that passes through (-2,0) and (1,-3) 5+ 4 3 2 1 -5-4-3-2-1 1 2 3 4 5 -1 --+ f(x) = -3- --4- -5+ 345 13.20 The expression log can be written in the form 218 A log(x) Blog (y) + Clog(2) where A = B = and C = A wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years. A house was valued at $120,000 in the year 1989. The value appreciated to $160,000 by the year 2006. Use the compound interest formula S = P(1+r)* to answer the following questions. A) What was the annual growth rate between 1989 and 2006? r = Round the growth rate to 4 decimal places. B) What is the correct answer to part A written in percentage form? r = %. C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2011 ? value = $ Round to the nearest thousand dollars. Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is t = | years. The count in a bacteria culture was 700 after 10 minutes and 1600 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 115 minutes. When will the population reach 12000. The fox population in a certain region has an annual growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 15500. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t)= | (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer should be an integer) Find an equation for the graph sketched below 8+ 7 6 5 4- 3+ 21 - + 54-3-2-1 1 f(x) = | -2- -3 -4 -5 -6- -7- -8- 2 3 4 5 The fox population in a certain region has a continuous growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 5500. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t) = || (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer must be an integer)