Question

The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given

Answer 1

Complete Question

The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given

by
`-(1)/(4) t-2`

where t is measured in years, how many cats are projected to be in the group in 2020.

Answer:

The number of total cats left after 8 years T

`T=76`

Explanation:

From the question we are told that

Number of cats 2012 n=100

Number of years t=2012-2020=>8 years

Generally the equation of change in population is mathematically Given as

`(dp)/(dt)= -(1)/(4) t-2`

`\int dp=\int_0^8 (-(1)/(4) t-2)`

`p=(-64)/(8) -16`

`p=-24cats`

Therefore the number of total cats left after 8 years T is given as

`T=100-24`

`T=76`