Answer:
The function y = 5 [tex](.98)^{x}[/tex] represents exponential decay
The percentage rate of change is 2%
Step-by-step explanation:
The formula of the exponential growth is y = a [tex](1+r)^{x}[/tex], where
- r is the rate of increase in decimal ⇒ (1 + r) > 1
The formula of the exponential decay is y = a [tex](1-r)^{x}[/tex], where
- r is the rate of decrease in decimal ⇒ (1 - r) < 1
Let us solve the question.
∵ y = 5 [tex](.98)^{x}[/tex]
→ Compare it with the forms above
∴ a = 5
∵ The rate of change is .98
∵ .98 < 1
→ That means the rate of change is decreasing
∴ The function y = 5 [tex](.98)^{x}[/tex] represents exponential decay
→ From the 2nd form above
∵ (1 - r ) = .98
→ Subtract 1 from both sides
∴ 1 - 1 - r = .98 - 1
∴ - r = - .02
→ Divide both sides by -1
∴ r = .02
→ Multiply it by 100% to change it to a percentage
∵ .02 × 100% = 2%
∴ r = 2%
∴ The percentage rate of change is 2%
