Question

The rat population in Hamlin is very prolific; the rats double their population every 2 days. An initial count of rats in the town shows 2048 rats.
(a) what is the rat population 10 days after the initial count?
(b) predict the population after 100 days
(c) write an equation that enables you to predict the rat population
(d) predict when the rat population will reach (1 million)

Answer 1

ok. now my brain is burning. Gimme a sec

Answer 2

A is 2097152.

Answer 3

the rest is too hard for me. Sorry.

Answer 4

Let Nt = population t days after the initial count.
\[N _{t}=2048\times (\sqrt{2})^{t}\]
After 10 days
\[N _{t}=2048\times (\sqrt{2})^{10}=65536\]
After 100 days
\[N _{t}=2048\times (\sqrt{2})^{100}=2.306\times 10^{18}\]

Answer 5

How can we find (c) and (d)???

Answer 6

Could you please explain to me where you got the square root of 2 ^x

Answer 7

The population doubles every 2 days. Therefore each day the population increases by the square root of 2.
The equation to predict the rat population is
\[N _{t}=2048\times (\sqrt{2})^{t}\]
where Nt is the population t days after the initial count.
If Nt = 1 million
\[10^{6}=2048\times (\sqrt{2})^{t}=2048\times 2^{\frac{t}{2}}\]
Rearranging and taking logs of both sides gives
\[\log_{} 488.28=\frac{t}{2}\times \log_{} 2\]
\[t=2\times \frac{\log_{} 488.28}{\log_{} 2}=you\ can\ calculate\]