We are given the formula
n(t) = no e ^ (rt)
no is the initial value
r is the growth rate
t is the time
a)
n(t) = 16000 e ^(.10 t)
b)
From 2013 to 2018 is 5 years so t =5
n(t) = 16000 e ^(.10 *5)
n(t) = 16000 e ^(.5)
=26379.54033
To the nearest whole number
= 26380
c)
25000 = 16000 e ^(.10 t)
25000/16000 = e^ .1t
25/16 = e ^ .1t
Taking the natural log of each side
ln ( 25/16) = ln ( e^(.1t))
ln(25/16) = .1t
Divide by .1
ln(25/16)/.1 = t
4.46287 = t
4.5 years = t
This is exponential growth
It is a curve going up starting at the amount of 16000