How do you write an exponential function whose graph passes through (0,-0.3) and (5,-9.6)?

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Answer 1 · 2016-11-03T17:06:39

Please see the explanation for steps leading to a solution.

An exponential function is:

#y = Ce^(alpha(x))#

We can find the value of C, using the point #(0, -0.3)#

#-0.3 = Ce^(alpha(0))#

#e^(alpha(0)) = 1# so we merely flip the equation and drop the exponential:

#C = -0.3#

We can use the point #(5, -9.6)# to find the value of #alpha#:

#-9.6 = (-0.3)e^(alpha(5))#

Divide both side by #-0.3#

#(-9.6)/(-0.3) = e^(alpha(5))#

#32 = e^(alpha(5))#

Take the natural logarithm of both sides, to make the exponential disappear:

#ln(32) = alpha(5)#

Divide both sides by 5:

#alpha = ln(32)/5#

The above is the same as #ln(root(5)(32)) = ln(2)#

#alpha = ln(2)#

The exponential function is:

#y = (-0.3)e^(ln(2)x)#