You are taking a biology class and you are growing a colony of bacteria starting with 5 bacteria. Suppose the colony of bacteria is grow exponentially and can be modeled using the following function:
$$B(t) = \frac{30}{{1+5}e^{-0.2t}}$$
How long will it take for you to triple (get 3 times) the initial population of the colony using natural log in the answer.
Process:
Since it asks for natural log, I know it needs the logarithm function.
I first added the 5 bacteria with the 3 to get 15 for t.
I then tried to isolate the exponent by itself:
$$B(15) = \frac{30}{{1+5e^{-0.2t}}}$$
$$B(450) = 5e^{-0.2t}$$
I then used the log function to get
$$0.2t = \ln^{-0.2t}$$
I know my answer is wrong. Any help please?
The left side of your first equation should be $15$, not $B(15)$ as it is the number of bacteria you are interested in. That is just notation. When you did the algebra you skipped steps, so I cannot tell what is wrong. $$15= \frac{30}{{1+5e^{-0.2t}}}\\ 1+5e^{-0.2t}=2\\ 5e^{-0.2t}=1\\ e^{-0.2t}=\frac 15\\ -0.2t=\log(\frac 15)\\ t=-5\log(\frac 15)$$