Question

Plz help me with this question

Answer 1

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 $(b)^{x}$, where

• a is the initial value

• 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 $(b)^{x}$

→ To find b use any values from the table to substitute x and y

∵ At x = 1, y = 91,800

∵ 91,800 = 90,000 $(b)^{1}$

∴ 91,800 = 90,000 b

→ Divide both sides by 90,000

∵ $\frac{91,800}{90,000}$ = $\frac{90,000b}{90,000}$

∴ 1.02 = b

→ Substitute it in the equation above

∵ y = 90,000 $(1.02)^{x}$

∴ The equation that models the population growth is y = 90,000(1.02)^x