Suppose the rate of growth of bacteria in a petri dish is given by q (t) = 12 t, where t is given in hours and q (t) is given in millions of bacteria per hour. If a culture starts with 89,000,000 bacteria, find a function q (t) that gives the number of bacteria in the petri dish at any time t. How many bacteria are in the dish after 3 hours

a) Q (t) = 89 + 12t

b) Q (3) = 125 millions of bacteria

Step-by-step explanation:

a)

to write a function of the growth of bacteria, we need to consider the initial population and add it to the new bacteria. Also we need to consider that the result of the function is in millions of bacteria, so when we get a result, we express it in millions.

Data

Initial population = 89 just add it to the function given 12t

Q (t) = 89 + 12t

b) Data time = 3 h

Q (3) = 89 + 12 (3) substitution

Q (3) = 89 + 36 simplifying

Q (3) = 125 millions of bacteria