Question

(a) Graph y=200(0.2)0.3x for x=0 to x=10.(b) What is the initial value of this function (the y-value when x=0)?(c) What is the limiting value of this function?

Answer 1

a)

To graph the function:

`y=200(0.2)^(0.3x)`

we need to give the x variable some values to get y, then we will have the point (x,y). For example if x=0 we have:

`y=200(0.2)^(0.3\cdot0)=0`

then we have the point (0,200).

If x=1 then:

`y=200(0.2)^(0.3\cdot1)=123.4067`

then we have the point (0,123.4067).

With this procedure we have the following table:

Plotting this points in the plane and joining them with a smooth line we have:

Comparing with the option given we conclude that the correct graph is B.

b)

From the table above we conclude that the initial value of the function is 200.

c)

From the graph we notice that as x grows the value of y gets smaller, this means that the limiting value will be zero.