how do I solve this/

Question

A colony of 100,000 bacteria grows exponentially to 400,000 in two hours. If this rate of growth continues, how many hours does the colony take to grow to 1,000,000 bacteria?

Answer 1

P=Poe^kt is the formula for exponential growth. Plugging in the values you have, you can solve for k. Then, use that value of k to predict the time it will take to get to 1,000,000.

400000=100000e^k(2) Dived both sides by 100000

4=e^k(2) Take the ln of both sides

ln 4 = 2k(ln e) ln e = 1. Divide both sides by 2 to get k

(ln 4)/2 = 2k/2

k=0.6931

Now the equation we have is

1000000=100000e^0.6931t This time we are solving for t, but the process is the same. Dived both sides by 100000

10=e^0.6931t Take the ln of both sides

ln 10=0.6931t (ln e) ln e = 1. Divide both sides by 0.6931 to get t

(ln 10)/0.6931=0.6931t/0.6931

t = 3.32 hours