Can someone help me with this problem?

Question

A colony of bacteria with initial population No grows exponentially, i e, total population N (T) after t days is N(T)= Noe^kt. if the initial population is 2000, and after 1 day the population grows to 3000. how many days will it take to reach 5000?

Answer 1

If you use days as units for t, then k will have units of (1/days). Keeping that in mind, we find that

3000=2000 e^k(1) ⇒ 1.5=e^k Now, we can solve for k. k=ln(1.5)= 0.405 / days.

Now, we will solve for t which is the time it takes for the population to grow to 5000. We write down the equation;

5000 = 2000 e^{0.405 t} and solve for t.

2.5 = e^{0.405 t}

ln(2.5) = 0.405 t

t = ln(2.5)/0.405

t = 2.26 days