37. [0/1 Points] DETAILS PREVIOUS ANSWERS BERRAPCALCBR7 4.2.007. MY NOTES ASK YOUR TEACHER Use the properties of natural logarithms to simplify the function. f ( x ) = In(x6) - In(x) f(x) = In(x5) X42. [0/2 Points] DETAILS PREVIOUS ANSWERS BERRAPCALCBR7 4.2.019. MY NOTES ASK YOUR TEACHER A bank offers 4% compounded continuously. How soon will a deposit do the following? (Round your answers to one decimal place.) (a) triple 28.0 X yr (b) increase by 21% 4.9 X yr 43. [0/1 Points] DETAILS PREVIOUS ANSWERS BERRAPCALCBR7 4.2.031. MY NOTES ASK YOUR TEACHER The proportion of carbon-14 still present in a sample after t years is e-0.00012t. + Estimate the age of cave paintings if the carbon with which they were drawn contains only 2.9% of its original carbon-14. (Round your answer to the nearest year.) 21764 X yr 44. [0/1 Points] DETAILS PREVIOUS ANSWERS BERRAPCALCBR7 4.2.033. MY NOTES ASK YOUR TEACHER The radioactive isotope potassium-40 is used to date very old remains. The proportion of potassium-40 that remains after t million years is e -0:00054. Use this function to estimate the age of the following fossil. A skeleton of an early human ancestor was discovered. Use the formula to estimate its age if rocks near the remains contained 99.75% of their original potassium-40. (Round your answer to one decimal place.) 200.9 X million years46. [0/1 Points] DETAILS PREVIOUS ANSWERS BERRAPCALCBR7 4.2.035. MY NOTES ASK YOUR TEACHER Hospitals use radioactive tracers in many medical tests. After the tracer is used, it must be stored as radioactive waste until its radioactivity has decreased enough for it to be disposed of as ordinary chemical waste. For the radioactive isotope iodine-131, the proportion of radioactivity remaining after t days is e-0.08/. How soon will the proportion of radioactivity decrease to 0.002 so that it can be disposed of as ordinary chemical waste? (Round your answer to the nearest day.) 137 x days