Please HELP me with this math PROBLEM?

Question

During surgery, a patient must have at leaset 40 mg of an antibiotic in his system. The amount of antibiotic presents k hours after administration of 100 mg of this antibiotic is given
by P(k)= 100(.508)^k. After how many hours (to the nearest tenth) will the nurse have to administer another dose of the antibiotic to keep the level of antibiotic high enough?

Answer 1

Just solve 1008(.508)^k = 40 on your calculator.

The simpler way to solve these is to convert the equation to logs.
Hint: a^n converts to n*log(a)