Abacteria culture grows with constant relative growth rate. after 2 hours there are 600 bacteria and after 8 hours the count is 75,000.
(a) find the initial population.
(b) find an expression for the population after t hours.
(c) find the number of cells after 3 hours.
(d) find the rate of growth after 3 hours.
(e) when will the population reach 200,000?

a) The initial population is 125 bacteria.

b)

c) There are 1378 cells after 3 hours.

d) The rate of growth after 3 hours is of 1102 cells an hour.

e) The population will reach 200,000 in 9.22 hours.

Step-by-step explanation:

The population of this culture can be modeled by the following formula:

In which P(t) is the population after t hours, is the initial population, and r, as decimal, is the growth rate.

(a) Find the initial population.

Also

Replacing in this equation:

Applying ln to both sides

The initial population is:

The initial population is 125 bacteria.

(b) Find an expression for the population after t hours.

(c) Find the number of cells after 3 hours.

There are 1378 cells after 3 hours.

(d) Find the rate of growth after 3 hours.

This is P'(3).

So

The rate of growth after 3 hours is of 1102 cells an hour.

(e) When will the population reach 200,000?

Applying ln to both sides

The population will reach 200,000 in 9.22 hours.

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it

step-by-step explanation: