Function/log problem. The number of bacteria in a petri dish culture after t hours is b(t)=100(3)^0.6934t?

Question

What is the initial number of bacteria present?

How many bacteria are present after 6 hours?

How long will it take for the number of bacteria to double?

Please help and thank YOU!

Answer 1

1) initial number is clearly 100. If you don't know why, just set t=0 and press calculator.

2) set t=6 and press calculator

3) set b(t)=200 and solve for t:

200 = 100 * 3^(0.6934t)

2 = 3^(0.6934t)

ln2 = 0.6934t ln3

t = ln2/(0.6934ln3)

Press calculator for t.