Use the equation of the exponential function whose graph passes through the points (0,-2) and (2,-50) to find.

Question

the value of y when x= -2

a. -1/100
b. 50
c. -2/25
d. -1/50

Answer 1

An exponential equation is of the form

y = amount
a = starting amount

y = ae^(kx)

Plugging in the first point we get:

-2 = ae^(k*0) = ae^0 = a*1 = a
a = -2

So now we have the equation:

y = -2e^(kx)

Now plug in the second point:

-50 = -2e^(2k)
25 = e^(2k)
ln25 = 2k
k = (ln25)/2

Now we have the equation:

y = -2e^[(1/2)(ln25) x]

Solve for y at x = -2.

y = -2e^[(1/2)(ln25)*(-2)] = -2e^(-ln 25)
y = -2*(-25) = 50

The answer is b. 50.

Answer 2

(0,-2)+(2,-50)

Answer 3

d.