Ask a New Question
Menu

Question

The population of Midtown grows about 2% each year. In 1990 the population of Midtown was 2050.
 
Which equation best represents the population, y, of Midtown x years after 1990?
Answer options with 4 options
A.
y equals 2050 left-parenthesis 0.02 right-parenthesis Superscript x Baseline
B.
y equals 2050 left-parenthesis 1.02 right-parenthesis Superscript x Baseline
C.
y equals 2050 plus 0.02 x
D.
y equals 2050 plus 1.02 x

1 answer

To model the population of Midtown which grows at a rate of 2% each year, we can use the formula for exponential growth, which is given by:

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

where:

  • \( P \) is the initial population,
  • \( r \) is the growth rate (as a decimal),
  • \( x \) is the number of years after the initial population was recorded.

In this case:

  • The initial population \( P \) in 1990 is 2050,
  • The growth rate \( r \) is 2%, which as a decimal is 0.02,
  • \( x \) is the number of years after 1990.

Plugging the values into the formula, we get:

\[ y = 2050(1 + 0.02)^x \] \[ y = 2050(1.02)^x \]

Therefore, the equation that best represents the population of Midtown \( y \) \( x \) years after 1990 is:

B. \( y = 2050(1.02)^x \)