To find the population of New Zealand in 10 years given a doubling time of 30 years, we can use the rule of exponential growth. The doubling time is the time it takes for a population to double in size at a constant growth rate. We can apply the formula for exponential growth, which is:
P(t) = P_0 * (2)^(t/T)
where:
- P(t) is the population at time t,
- P_0 is the initial population,
- t is the time that has passed,
- T is the doubling time.
Given that:
- The initial population, P_0, is 6,000,000,
- The doubling time, T, is 30 years,
- And we want to find the population in 10 years (t = 10).
Let's plug these values into the formula:
P(10) = 6,000,000 * (2)^(10/30)
Now, we need to calculate the exponent:
10/30 = 1/3
So we have:
P(10) = 6,000,000 * (2)^(1/3)
Now, 2^(1/3) means the cube root of 2, which is approximately 1.259921. We can then multiply the initial population by this growth factor:
P(10) = 6,000,000 * 1.259921
P(10) ≈ 6,000,000 * 1.259921
P(10) ≈ 7,559,526
Therefore, if New Zealand's population growth continues at the same rate, the population in 10 years will be approximately 7,559,526.
