Step-by-step explanation:
remember :
linear functions are
f(x) = y = ax + b
exponential functions are
f(x) = y = a×(b^x)
so, for linear functions
f(0) = b
and f(n) - f(n-1) is
an + b - (a(n-1) + b) = an - an + a = a
for exponential functions
f(0) = a
and
f(n)/f(n-1) is
(a×b^n)/(a×b^(n-1)) = (b^n)/(b^(n-1)) = b
we need to check, what are the actual measurements cost to :
is the relationship between f(n) and f(n-1) more like adding a fixed constant for the same increase of x, or is it more like a multiplication by a fixed constant fire the same increase of x ?
x = 5
f(5) - f(0) = 22
f(5)/f(0) = 454/432 = 1.050925926...
x = 10
f(10) - f(5) = 45
f(10)/f(5) = 499/454 = 1.099118943...
x = 15
f(15) - f(10) = 35
f(15)/f(10) = 534/499 = 1.070140281...
x = 20
f(20) - f(15) = 48
f(20)/f(15) = 582/534 = 1.08988764...
x = 25
f(25) - f(20) = 29
f(25)/f(20) = 611/582 = 1.049828179...
the data shows us :
the differences are going smaller, larger, smaller, larger and don't seem to indicate a constant.
but the ratios of the differences are close varying maybe by about 4%, indicating a constant factor at around 1.075.
so, this looks definitely like a candidate for an exponential regression model.
