How do you write an exponential equation that passes through (0, -2) and (2, -50)?

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Answer 1 · 2016-02-13T17:58:02

You set #f(x)=a*e^(bx)# and find the #a# and #b# constants via the 2 passing points.

#f(x)=-2*e^(ln25/2*x)#
or
#f(x)=-2*e^(1.60944*x)#

Let the exponential function be:

#f(x)=a*e^(bx)#

where #a# and #b# are constants to be found. From the two points that the function is passing we know that:

Point (0,-2)

#f(0)=-2#

#a*e^(b*0)=-2#

#a*1=-2#

#a=-2#

Point (2,-50)

#f(2)=-50#

#-2*e^(b*2)=-50#

#e^(2b)=(-50)/-2#

#e^(2b)=25#

#lne^(2b)=ln25#

#2b=ln25#

#b=ln25/2=1.60944#

Function

So now that the constants are known:

#f(x)=-2*e^(ln25/2*x)#
or
#f(x)=-2*e^(1.60944*x)#