A colony of 5 bacteria doubles in size every 150 hours. What will the population be 450 hours from now?

Question

I DONT GET HOW EXPONENTIAL GROTH AND DECAY WORKS I NEED SOME HELP PLEASE....

 

Answer 1

I hope you know the formula A=Pe^rt which works for growth and decay of money and populations.

 

P is the principal....what you start with

A is the final amount

r is the rate

t is the time

e is a number approximately equal to 2.718

 

so if you start with 5, it doubles to 10 in 150 hours means

10 = 5e^150r  divide by 5 to get

 2 =  e^150r   take the ln of both sides to get

ln 2 = 150r   divide by 150 to get

(ln2)/150 = r = .004620981204

 

You can now plug that in as the constant rate of growth to get the formula.

 

A = 5e^{.004620981204*t}

So now you can plug in t=450 and evaluate to get 40.

 

now you can check this by setting up a table

 

population      hours

5                     0

10                  150

20                   300

40                  450

80                   600

 

For every 150 hours, the population doubles.

 

Hope this helped.