Find a formula for an experienced equation that goes through the points

(x,y)=(-2,50) and (x,y)=(0,2)
Express the formula as an equivalent equation with base e.
y=

1 answer

To find the formula for the experienced equation that goes through the points (-2,50) and (0,2), we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, we can find the slope:

m = (y2 - y1) / (x2 - x1)
m = (2 - 50) / (0 - (-2))
m = -24

Using the point-slope form with the point (-2,50):

y - 50 = -24(x - (-2))

Simplifying:

y - 50 = -24(x + 2)
y - 50 = -24x - 48
y = -24x + 2

To express this equation with base e, we can use the natural logarithm:

ln(y) = ln(e^(-24x+2))

Simplifying:

ln(y) = -24x + ln(e^2)
ln(y) = -24x + 2ln(e)
ln(y) = -24x + 2

Therefore, the equivalent equation with base e is:

y = e^(-24x+2)