g(x) = a b^x
25 = a b^30
40 = a b^10
a = 25/b^30
a = 40/b^10
so
25/b^30 = 40/b^10
40/25 = b^10/b^30
1.6 = b^10/b^30
ln 1.6 = ln b^10 - ln b^30 = 10 ln b -30 lb b = -20 ln b
ln b = -.470/20 = -.0235
b = .9768
now
25 = a b^30= a(.494)
a = 50.6
so
g(x) = a b^x
is
g(x) =50.6 *.9768^x
================== now check
if x = 10
g(10) = 50.6 * .9768^10
g(10) = 40 whew :)
Find a formula for the exponential function which satisfies the given conditions:
g(10)=40 and g(30)=25.
g(x)=
1 answer
1 answer