1) Condense the following into a single logarithmic expression:

3log(x +1) + 5log(9x +1) - log(x+1)

2) $52,000 is invested in an account at interest rate r = 5.1%, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.)

3) The populations P (in thousands) of Carson, Nevada from 2000 through 2007 can be modeled by

P(t) 346e^kt

where t represents the year, with t = 0 corresponding to 2001. In 2007, the population of Carson was about 395,000. According to the model, during what year will the population reach 480,000?

4) Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is 14C is constant. The amount of 14C in an object made from harvested plants, like paper, will decline exponentially according to the equation:

A = A₀e^-0.000111t

where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 55% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.