Question

A factory began dumping toxic waste materials into a countryside lake. Before the dumping began, the estimated population of striped bass in the lake was 40,000. Since the dumping of toxic waste materials began, the population has decreased by one-half every month. Determine the equation that represents this situation and use it to decide which of the following graphs represents the population of striped bass, f(x), x months after the factory began dumping toxic waste materials into the lake.

Answer 1

The answer is Y I think

Answer 2

Answer:

$f(x)=40000(\frac{1}{2})^{x}$ and Graph X.

Step-by-step explanation:

Estimated population of striped bass in the lake was 40000.

After dumping of toxic waste materials from the factory population has decreased by one half every month.

So we can represent the sequence month by month as

$a, a(\frac{1}{2}), a(\frac{1}{2})^{2}, a(\frac{1}{2})^{3}.....$ upto x months.

Now the explicit formula of this sequence will be

$T_{x}=a(r)^{x}$

Here a is the initial population = 40000

Common ratio = $\frac{\frac{a}{2}}{a}=\frac{1}{2}$

So explicit formula will be

$f(x)=40000(\frac{1}{2})^{x}$

When we graph the function points on the graph will be

(0, 40000), (1, 20000), (2, 10000)

These points lie on a curve given in graph X, which is the graph of exponential function.

Therefore the answer will be Graph X.