Question

Problem: Using the doubling time growth model, what will the population for a city be in 4 years if the current population is 750,000 and the doubling time is 36 years?

Step 1: What equation in terms of the variables P0, t, and d would you use to solve this problem? Use your keyboard and the keypad to enter your answer.

Answer 1

Pt = P02^ (t/d)

Explanation:

P0 gives the original population. It is multiplied by 2 to the power td. The variable d is the known doubling time, and t is the number of years passed since the population was P0. So you get Pt = P02 ^ (t / d).

Answer 2

The population of the city in 4 years is approximately 810,032

Explanation:

The doubling time growth model is still an exponential model, albeit, a very special one

P(t) = P₀ eʳᵗ

P(t) = Population at any time

P₀ = Initial Population for the city

t = time in years from the initial time when the population P₀ was recorded

r = rate constant, it seems r = d according to the step 1 of the question.

P(t) = P₀ eʳᵗ = P₀ eᵈᵗ

In a doubled time, t = 36 years, P(t) = 2P₀

2P₀ = P₀ eʳᵗ

eʳᵗ = 2

In eʳᵗ = In 2 = 0.693

rt = 0.693

r = (0.693/t)

Note that this time is the doubling time, t = 36 years

r = d = (0.693/36) = 0.01925

So, to solve the question now,

P(t) = P₀ eʳᵗ

P(t) = P₀ e⁰•⁰¹⁹²⁵ᵗ

P₀ = 750,000

t = 4 years

P(t) = ?

0.01925t = 0.01925 × 4 = 0.077

P(t=4) = 750000 e⁰•⁰⁷⁷

= 810,031.55729445 = 810,032

Hope this Helps!!!