Write an expression, of the type A log(x + B) or A log(-(x+B)), for the transformed logarithmic function shown below: 6 5 4 3 2 -6-543-A-L + --x 3- -4 -5 3 f(x)= Hint: Use the vertical asymptote to find B. To solve for A, use a point on the graph and substitute the coordinates into: y = A log(x + B) or y = A log(-(x+B)), as appropriate. 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? 32 What is the mass 8 weeks after the start? 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 $174000 Round to the nearest thousand dollars. 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. 16.77 Find the population after 115 minutes. 53442 When will the population reach 12000. 78.86 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 + 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)