Calculate, using the properties of logarithms:
Figure out which of these logarithms are easy to evaluate without a calculator. Give an exact answer for those questions. For the remaining questions, approximate the answer to three decimals. Use the log-button of your calculator to do so.
A radioactive substance decays according to the formula:
is the amount in mg and is the time in years.
What is the half-time of this substance?
A laboratory has a stock of g of this substance. Calculate, using the half-time, how long it takes for the amount of original material to become less than g.
Calculate to the month how long it takes for g of original substance to become less than g.
The radioactive isotope calcium-45 has a half-time of days.
After what time has any quantity of calcium-45 been reduced to of its original amount?
After what time has any quantity of calcium-45 been reduced to of its original amount?
A laboratory has a stock of grams of calcium-45. Estimate, using your answers from parts a and b, how long it would take for this stock to contain less than grams of calcium-45.
Calculate a precise answer to c (in days).
A quantity is growing exponentially with a growth percentage of percent.
Show that the doubling time is given by .
Solve the following equations algebraically. Give approximate answers, rounded to one decimal.