Question

A bee population is measured each week and the results are plotted on the graph

Answer 1

The first measurement correspond to week=0, and the bee population is B(0)=500.

We can construct a table with the values as:

w | B(w)

0 | 500

1 | 1000

2 | 2000

3 | 4000

Each week, the bee population is growing by the same factor:

$B(w+1)=2\cdot B(w)$

The bee population is doubling each week.

We can model this relation as an exponential growth:

$B(w)=A\cdot C^w$

We can find the values of the parameters using the values from the graph:

$B(0)=A\cdot C^0=A\cdot1=A=500$$\begin{gathered} B(1)=500\cdot C^1=1000 \\ C=\frac{1000}{500}=2 \end{gathered}$

Then, the equation that relates bee population B and weeks w is:

$B(w)=500\cdot2^w$

Answer:

1) 500

2) We can find that the population is doubling by calculating the ratio between the populaiton of consecutive weeks. The qoutient B(w+1)/B(w) is always equal to 2, so the bee population is doubling.

3) The equation is B(w) = 500*2^w