The population of Logland is 1200 in 2010, and the population increases each year by 12%. What equation is used to determine the population, y, of Logland x years after 2010? Enter your answer by filling in the boxes.

To determine the population, y, of Logland x years after 2010, using the given increase rate of 12% each year, we can use the formula for exponential growth:

[ y = P(1 + r)^x ]

Where:

- ( y ) is the population of Logland x years after 2010 (which we want to find)

- ( P ) is the initial population in the base year 2010, which is 1200

- ( r ) is the growth rate, which is 12% or 0.12 when written as a decimal

- ( x ) is the number of years after 2010

Substitute these values into the formula:

[ y = 1200(1 + 0.12)^x ]

This equation can be used to determine the population of Logland x years after 2010

msm555 msm555 · Answer 2 · 2024-03-22T16:41:43+01:00

Answer:

[tex] y = 1200 \times (1 + 0.12)^x [/tex]

Step-by-step explanation:

To determine the population [tex] y [/tex] of Logland [tex] x [/tex] years after 2010, we can use the exponential growth formula:

[tex] \Large\boxed{\boxed{y = y_0 \times (1 + r)^x}} [/tex]

Where:

[tex] y_0 [/tex] is the initial population (in 2010), which is 1200.
[tex] r [/tex] is the growth rate per year, which is 12% or 0.12 as a decimal.
[tex] x [/tex] is the number of years after 2010.

Substituting the given values into the formula:

[tex] y = 1200 \times (1 + 0.12)^x [/tex]

So, the equation used to determine the population [tex] y [/tex] of Logland [tex] x [/tex] years after 2010 is:

[tex] \boxed{y = 1200 \times (1 + 0.12)^x} [/tex]