Question

If you don't brush your teeth regularly, it won't take long for large colonies of bacteria to grow in your mouth. Suppose that a single bacterium lands on one of your teeth and starts reproducing by a factor of 4 every 4 hours
A) Write an equation that describes the number of bacteria b in the new colony after n hours.
B) How many bacteria will be in the new colony after 7 hours, 8 hours?
C) After how many hours will there be at least 1 million bacteria in the new colony?

Answer 1

D) Suppose that 50 bacteria, not just 1 bacterium, land in your mouth. Write an equation that describes the number of b in this colony after n hours.

Answer 2

This topic is expo/log application, growth and decay.

Answer 3

our original equation is f(t) = Ae^kt to the base 0

Answer 4

A to the base 0 = initial amount of t = 0
t = time
k = growth constant, k>0
decay constant, k<0

Answer 5

b = A*e^(kt)
A=1 (one bacterium)
when t=4
b=4
ln 4 = kt*ln e
ln 4 = k4* ln e
k= (ln4)/4

Answer 6

woah, you're good!

Answer 7

but can you explain to me how you got those values/equations?

Answer 8

sure. what's your question?

Answer 9

ok first, this might sound stupid but what is the symbol on Top of A?

Answer 10

this * ?

Answer 11

yes

Answer 12

it means multiplication.

Answer 13

alright :D thanks!

Answer 14

how did you get the equation?

Answer 15

from you.

Answer 16

"our original equation is f(t) = Ae^kt to the base 0 "

not sure what you mean by 'base 0', but the rest is correct.

Answer 17

cause our teacher said this is the equation: