Question

A a population shrinks from its initial level of 20,000 at a continuous decay rate of 7.1% per year. (a) Find a formula for P(t), the population in t years. P(t)= help (formulas) (b) By what percent does the population shrink each year? % (Round to the nearest 0.001%) help (numbers) 4​

Answer 1

The population formula is P(t) = 20,000e^-0.071t, representing exponential decay at a continuous rate of 7.1% per year.

The population shrinks by 7.1% each year.

Step-by-step explanation:

To find the formula for P(t), the population in t years, given an initial population of 20,000 and a continuous decay rate of 7.1% per year, we can use the exponential decay model:

P(t) = P0e^-rt,

where:

• P0 is the initial population,
• e is the base of the natural logarithm,
• r is the decay rate per unit of time,
• t is the time in years.

Plugging in the given values:

P(t) = 20,000e^-0.071t.

Yearly Shrinkage Percentage:

• The population shrinkage percentage is the decay rate expressed as a percentage.

• In this case, it is 7.1% each year.