Question

SOLVE ALGEBRAICALLY!!!

The population trend for Berthoud, CO, can be represented by the function P(t) = 106.67t + 4763.67, and the population trend for Wellington, CO, can be represented by the function P(t) = 308.8t + 2844.18 where t is the time in years since 2000. When will the towns have the same population?

Answer 1

9.5 years

Explanation:

P(t) = P(t)

106.67t+4763.67=308.8t+2844.18

Minus 106.67t on both sides

4763.67=202.13t+2844.18

Minus 2844.18 on both sides

1919.49=202.18t

Solve for t

t=9.4963...

t=9.5 years

Answer 2

To find when the towns of Berthoud and Wellington will have the same population, we can set their population functions equal to each other and solve for the value of t:

106.67t + 4763.67 = 308.8t + 2844.18

First, let's rearrange the equation by moving all the terms involving t to one side:

106.67t - 308.8t = 2844.18 - 4763.67

Simplifying the equation gives:

-202.13t = -1921.49

Now, we can isolate t by dividing both sides of the equation by -202.13:

t = (-1921.49) / (-202.13)

Solving this equation yields:

t ≈ 9.51

Therefore, the towns of Berthoud and Wellington will have the same population approximately 9.51 years after 2000.