Question

The population of a species in a preserve is 800. The population is expected to decrease at a rate of 2% each year.

What function equation represents the population of the species after t years?

Enter your answer by filling in the boxes.

Answer 1

P(t) = 800 * 0.98^t

Explanation:

If the population of a species in a preserve is 800, and it is expected to decrease at a rate of 2% each year, we can use the exponential decay model to represent the population after t years:

P(t) = P (1 - r)^t

P = initial population (800 in this case)

r = decay rate (2% or 0.02 as a decimal)

t = time

Substituting the given values into the formula, we get:

P(t) = 800 * (1 - 0.02)^t

P(t) = 800 * 0.98^t

So, the equation is P(t) = 800 * 0.98^t

Answer 2

The equation for exponential decay is given by:

• 
  `y = a(1-r)^t`

where:

• y = the population after t years
• a = the initial population (
  `800`)
• r = the rate of decrease (
  `2\%` or
  `0.02`)
• t = the number of years

Substituting the given values, we get:

• 
  `y = 800(1-0.02)^t`

Simplifying this equation, we get:

• 
  `\boxed{y=800(0.98)^t}`

`\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}`