Question

Two of the most dangerous animals in the enchanted forest are snakes and bears. The population of bears began with 100 bears in the year 2000 and increases at a rate of 4 bears per year. The population of snakes began at 1 snake in the year 2000 and doubles every year.
Do you think the population of snakes will ever catch up to the population of bears? Why or why not?
If you answered yes, how many years do you think it would take for snakes to outnumber bears?

Answer 1

Answer:

Yes

IT WILL TAKE 8 YEARS.

Step-by-step explanation:

Bear starting population = 100

Bear population rate = 4 per year

Snake starting population = 1

Snake population rate = doubles every year

Bear population model:

y = 4x+100

Where y = new bear population

x = number of years after year 2000

Snake population model :

y = 2^x

Where y = new snake population

x = number of years after year 2000

THE POPULATION OF SNAKES WILL CATCH UP WITH THAT OF BEARS BECAUSE AFTER 7 YEARS THE POPULATION WILL BE EVEN.

After 7 years :

Bear population :

y = 4x + 100

y = 4(7) + 100 = 128

y = 128

Snake population :

y = 2^x

y = 2^7

y = 128

Using random guess in the both models :

After 8 years :

Bear population :

y = 4x + 100

y = 4(8) + 100 = 132

y = 132

Snake population :

y = 2^x

y = 2^8

y = 256