Question

The current population of a threatened animal species is 1.3 million, but it is declining with a half-life of 25 years. How many animals will be left in 35 years? in 80 years?Question content area bottom(Round to the nearest whole number as needed.)

Answer 1

Given:

it is given that the current population of a threatened animal species is 1.3 ​million, but it is declining with a​ half-life of 25 years.

Find:

we have to find that how many animals will be left in 35 years and in 80 years.

Step-by-step explanation:

we know 1.3million = 1300000

The decay law is

`P(t)=1300000*((1)/(2))^{(t)/(25)}`

where t is in years and p(t) is the population at time t.

Now, the number of animals left in 35 years is

`\begin{gathered} P(35)=1300000*((1)/(2))^{(35)/(25)} \\ P(35)=1300000*((1)/(2))^(1.4) \\ P(35)=492608(by\text{ rounded to nearest whole number\rparen} \end{gathered}`

Therefore, 492608 animals will be left in 30 years.

Now, the number of elements left in 80 years is

`\begin{gathered} P(80)=1300000*((1)/(2))^{(80)/(25)} \\ P(80)=1300000*((1)/(2))^(3.2) \\ P(80)=141464(by\text{ rounded to nearest whole number\rparen} \end{gathered}`