The population of Adamsville grew from 7,000 to11,000 in 77 years. what is the expected population in an additional 55 ​years?

Question

Justneed to know the expected population

Answer 1

Since the topic is exponential growth, I'll sassume an exponential growth model:

 

P(t) = P₀·b^t

• P(t) = population in year t
• P₀ = starting population
• b = growth rate
• t = years

 

P(t) = P₀·b^t

 

We have two (t, P(t)) data points, (0, 7000) and (77, 11,000).  Plugging in (0, 7000):

 

7000 = P₀·b⁰

7000 = P₀

 

So the equation so far is P(t) = 7000·b^t.  To find b, plug in the second data point (77, 11,000):

 

11,000 = 7000·b⁷⁷

11/7 = b⁷⁷

(11/7)^1/77 = b

 

So the final equation is P(t) = 7000·(11/7)^t/77.  In an additional 55 years, after the 77 years, we have t = 77 + 55 = 132 years (from t=0).  Plug t = 132 into the final equation and use your calculator to get the answer.  Round down to the nearest whole person.