1.) The population at timetis given by the equation below. Find a formula that gives the time it takes for the population todouble. (This problem deals with functions of the form f(x)=P_e^kx, wherekis the continuous exponential growth rate.) S(t)=ce^kt

^{t=________. show your work.}

^2.) Between 1996 and 2004, the number of subscribers to cell-phone plans has grown nearly exponentially. In 1996 there were45,178,000subscribers and in 2004 there were172,421,000. (This problem deals with functions of the form f(x)=P_e^kx wherekis the continuous exponential growth rate.)

(a) What is the continuous growth rate of the number of cell-phone subscribers? (Round your answer to four decimal places.) (b) In what year were there 70,000,000 cell-phone subscribers? (c) Assuming that this rate continues, in what year will there be 310,000,000 subscribers?

3.) The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. How old is a mummy that has lost 52% of its carbon-14 (its half-life is 5730 years)? (Round your answer to the nearest year.)

M(x)= c(.5^x/h)

________ years? Show your work.

4.) The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. The half-life of a substance is 6.4 years. How long will it take for 85 grams to decay to 28 grams? (Round your answer to one decimal place.)

M(x)= c(.5^x/h)

________ years? Show your work.

5.) Solve the equation. First, express your answer in terms of natural logarithms (for instance,x= (2 + ln(5)) / (ln(3)). 21e^-x/3=67.6

x=______________? Show your work.

6.) Solve the equation. First, express your answer in terms of natural logarithms (for instance, x = (2 + ln(5)) / (ln(3)).

7^x-4=6^x-3

x=_______________? Show your work.