A biologist is growing bacteria for a lab experiment. There are 10 mg of bacteria in a controlled environment when she changes the temperature. The amount P of bacteria then grows at a rate of P'(t) = 20(0.95)^t per hour where t is the number of hours since the temperature changed

(a) Write an integral that models the amount of bacteria at time t > 0.
(b) Find the amount after 24 hours.

a) 389.915, b) 276.064.

Explanation:

Since we have given that

where t is the number of hours since the temperature changed.

(a) Write an integral that models the amount of bacteria at time t > 0.

(b) Find the amount after 24 hours.

It means 0<t < 24

Hence, a) 389.915, b) 276.064.

"1. it should be, it has been for about 20 years, and it's really not much different in the end than breeding animals to have particular traits. there are always concerns about genetically engineered animals/plants affecting the environment in unexpected negative ways, but i can't think of an example where the fears didn't turn out to be baseless.  

first, as you point out, it would be a great advance in pharmacology, to be able to tailor drugs and their doses to me. the pros involve better medical treatment. the cons involve privacy issues like insurance companies denying coverage to people with genetic risk factors. looking at dna markers wouldn't affect the frequency of genetic diseases, but it would allow detection of them earlier. and ok, actually i suppose that if people used this information to avoid having children with genetic diseases, some might decrease in frequency."