Bacteria modeling populations

Is the population growing continuous or is the population doubling? If the population is continuous, we use the base \(e\).

\(y=ae^{nt}\)

Where \(a\) is the initial population of 100, \(n\) is the number of days, and \(t\) is the rate (we need to find this):

\(y=100e^{nt}\)

Start by sub'ing in 150 in for \(y\) and \(100\) in for \(n\), leaving \(t\) blank:

\(150=100e^{100t}\)

Solve for \(t\):

\(\frac{150}{100}=e^{100t}\)

\(\ln{1.5}=100t\)

\(\frac{\ln{1.5}}{100}=t\)

\(t=4.05\times10^{-3}\)

Now our equation has a rate of \(t=4.05\times10^{-3}\):

\(y=100e^{n(4.05\times10^{-3})}\)

Sub'ing in \(n=150\)

\(y=100e^{150\cdot(4.05\times10^{-3})}\)

\(y=183.7\)

Round this 184 people after 150 days.

Please confirm if this is the correct strategy that was taught in class, otherwise we'll have to tackle this another way.

Talk soon