Question

A biologist recorded the population growth of two species of frogs in a pond area starting in 2010. The first species started with 42 frogs and increased by 6 frogs per year. The second species started with 30 frogs and increased by 8 frogs per year.

make an equation modeling equal populations of the frogs at T years after 2010.

Answer 1

Answer:

42 + 6t = 30 + 8t

Step-by-step explanation:

1st species starts with 42f. They gain 6 frogs a year, with the letter 't' representing years. 42 + 6t would be the rate for the first species. 2nd species starts with 30 and gains 8 frogs a year, the letter 't' also representing years. So 30 + 8t would be the rate. Writing an equation to find when the groups are equal, it would result in 42 + 6t = 30 + 8t

To find the answer to this,

42 + 6t = 30 + 8t

Step 1: Subtract 30 from both sides

42-30 +6t = 30-30 + 8t

12 + 6t = 8t

Step 2: subtract 6t from both sides

12 + 6t-6t = 8t-6t

12 = 2t

Step 3: divide both sides by 2

12/2 = 2t/2

6 = t

Step 4 : Rearrange

t = 6

Answer = 6