Question

An alligator population in Florida's Cedar Grove State Park is given by A = 3t² - 16t+ 1, where A is alligator population in hundreds and t is in years since 1995. When were there 3600 alligators in the park? ​

Answer 1

...The alligator population in Cedar Grove State Park in Florida is given by A = 3t² - 16t+ 1, where A is the alligator population in hundreds and t is the number of years since 1995. When were there 3,600 alligators in the park?

3t²-16t+1=36

3t²-16t+1-36=0

3t²-16t-35=0

b²-4ac = (-16)²-4(3*-35)=676

delta = 676,

Δ is strictly positive, so the equation 3x²-16x-35=0has two solutions

(-b-√Δ)/2a = (16-26)/6=5/3

(-b+√Δ)/2a =(16+26)/6=7

we're looking for a number of years, only 7 is suitable

7 years ago, in 1988, there were 3600 alligators in the park

Explanation: