How do you find the formula of an exponential graph given (0,4) and (1,4.3)?

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Answer 1 · 2016-09-01T06:13:06

#f(x) = 4(1.075^x)#

We want to fit these data points to a function of the form:

#f(x) = a*b^x#

for some constants #a, b# to be determined, with #b > 0#.

We are told:

#{ (f(0) = 4), (f(1) = 4.3) :}#

For any non-zero value of #b#, we have #b^0 = 1#.

So we find:

#a = a*b^0 = f(0) = 4#

#b = (a*b^1)/a = f(1)/a = 4.3/4 = 1.075#

So:

#f(x) = 4(1.075^x)#