Answer:
To find the equation of the form P = P₀aᵗ, we need to determine the values of P₀ and a.
Given that the population was 4.454 billion in 1980 (t = 0) and 5.931 billion in 1998 (t = 18), we can use these data points to find the values of P₀ and a.
Using the formula P = P₀aᵗ, we can set up two equations:
4.454 = P₀a⁰
5.931 = P₀a¹⁸
Since a⁰ is equal to 1, the first equation simplifies to:
4.454 = P₀
Substituting this value into the second equation, we have:
5.931 = 4.454a¹⁸
To solve for a, we can divide both sides of the equation by 4.454 and then take the 18th root:
a = (5.931 / 4.454)^(1/18)
Simplifying this expression, we find:
a ≈ 1.014
Therefore, the equation of the form P = P₀aᵗ, representing the world's population, is:
P = 4.454 * (1.014)^t
Explanation:
Let's break it down step by step:
1. We have two data points: the population in 1980 (4.454 billion) and the population in 1998 (5.931 billion).
2. We want to find the equation of the form P = P₀aᵗ, where P is the population in billions and t is the number of years since 1980.
3. Using the first data point, we know that when t = 0 (1980), the population is P₀. So, P₀ = 4.454 billion.
4. Using the second data point, we can substitute the values into the equation and solve for a: 5.931 = 4.454a¹⁸.
5. To solve for a, we divide both sides of the equation by 4.454 and then take the 18th root: a = (5.931 / 4.454)^(1/18).
6. Simplifying the expression, we find that a is approximately equal to 1.014.
7. Therefore, the equation of the form P = P₀aᵗ representing the world's population is: P = 4.454 * (1.014)^t.
I hope this helps! Let me know if you have any other questions.