Answer:
The equation that models the population growth is y = 90,000(1.02)^x
Step-by-step explanation:
The formula of the exponential growth is y = a [tex](b)^{x}[/tex], where
- b is the factor of growth ⇒ b > 1
Let us solve the question
∵ At x = 0, the population y = 90,000
→ That means the initial value is 90,000
∴ a = 90,000
→ Substitute it in the form of the equation above
∴ y = 90,000 [tex](b)^{x}[/tex]
→ To find b use any values from the table to substitute x and y
∵ At x = 1, y = 91,800
∵ 91,800 = 90,000 [tex](b)^{1}[/tex]
∴ 91,800 = 90,000 b
→ Divide both sides by 90,000
∵ [tex]\frac{91,800}{90,000}[/tex] = [tex]\frac{90,000b}{90,000}[/tex]
∴ 1.02 = b
→ Substitute it in the equation above
∵ y = 90,000 [tex](1.02)^{x}[/tex]
∴ The equation that models the population growth is y = 90,000(1.02)^x
