Question

We have a population of 200 people with a growth rate of 2%. Which equation do we use to calculate how long it will take for the population to double to 400 people? 70/.2 200/,2 200x2 400/2 70/2 70/.02 200/.02 200x.02 200/2

Answer 1

Answer:

70/2

Step-by-step explanation:

We have a population of 200 people

Growth rate = 2%

How long it will take for the population to double

Double the population = 2× 200 = 400

The formula for Exponential growth =

y = a(1 + r)^t

y = Value at time t = 400

a = Initial value = 200

r = 2% = 0.02

t = ?

Hence:

400 = 200 ( 1 + 0.02)^t

Divide both sides by 200

400/200 = 200 ( 1 + 0.02)^t/200

2 = (1.02)^t

Take logarithm of both sides

log 2 = log(1.02)^t

log 2 = t log 1.02

t = log 2/log 1.02

t = 35.003417942

Approximately t = 35

We have so many formula to calculate doubling time

t = 70/Growth rate

From the above question

Growth rate = 70/2%

= 35

Therefore, the equation that we use to calculate how long it will take for the population to double to 400 people is 70/2