Question

He population of a region is growing exponentially. there were 40 million people in 1980 (when t=0) and 55 million people in 1990. find an exponential model for the population (in millions of people) at any time t, in years after 1980.

Answer 1

P(t) = 40(2)^(kt)
when t=10, (1990), N = 55
55 = 40(2)^(10k)
1.25 = 2^(10k)
take the ln of both sides, hope you remember your log rules
10k = ln 1.25/ln 2
10k = .32193
k = .032193

so P(t) = 40(2)^(.032193t)

in 2000, t = 20
P(20) = 40(2)^(.032193(20))
= 62.5 million

for the formula
P(t) = a(2)^(t/d), d = the doubling time
so changing .032193t to t/d
= .032193t
= t/31.06

so the doubling time is 31.06

another way would be to set
80 = 40(2)^(.032193t)
2 = (2)^(.032193t)
.032193t = ln 2/ln 2 = 1
t = 31.06