Question

if f is an exponential function, and f(5)=20 and f(9) = 14, use the add-multiply property to calculate f(13),f(17), and f(21). Show your method

Answer 1

there is a difference of x=+4 between 5, 9
There is a multiply difference of 14/20=.7 between the two.

f(13)=14*.7
f(17)=14*.7*.7
f(21)=14(.7*.7*.7)

Answer 2

let f(x) = a(b^x) or
y = a(b^x)
given: when x=5, y=20
20 = a b^5
given: when x=9, y=14
14 = a b^9
divide the 2nd by the first:
b^4 = 14/20 = 0.7
b = (0.7)^.25 = appr .91469
sub into 20 = a b^5
20 = a(.91469)^5
a = 31.236
f(x) = 31.236 (.91469)^x

f(13) = 31.236(.91469)^13 = 9.8
you do the button-pushing for the rest

Note, I used the memory locations of my calculator to store all the supplied decimal values for both a and b