Question

Equation for this? I don't know

Answer 1

Given

• an exponential curve with points (-3, 12) and (-2, 7)
• a horizontal asymptote of y=2

Find

• the equation of the curve

Solution

Since the horizontal asymptote of a plain exponential curve is y=0, your curve has been shifted up 2 units. So, we know the function is something of the form ...

... y = 2 + a·b^x

Putting in the given point values, we have

... 12 = 2 + a·b^(-3)

... 7 = 2 + a·b^(-2)

Subtracting 2 from each of these equations and finding their ratio gives

... (12-2)/(7-2) = (2+a·b^(-3) -2)/(2+a·b^(-2) -2)

... 10/5 = b^-1 . . . . . simplify

... b = 2^(-1) = 1/2

Then we can use either of the given data points to find a.

... 12 = 2 + a·(1/2)^(-3)

... 10 = 8a

... 10/8 = a = 1.25

So, the equation for the curve is ...

... y = 2 + 1.25·0.5^x