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? a. $y = 2050(0.02)^x$ b. $y = 2050(1.02)^x$ c. $y = 2050 + 0.02x$ d. $y = 2050 + 1.02x$

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth is \( y = a(1 + r)^x \), where \( a \) is the initial amount, \( r \) is the growth rate (in decimal), and \( x \) is the number of time periods.

Step2: Identify values for the formula

Here, the initial population (in 1990) \( a = 2050 \). The growth rate is 2% per year, so \( r = \frac{2}{100}= 0.02 \).

Step3: Substitute values into the formula

Substituting \( a = 2050 \) and \( r = 0.02 \) into the exponential growth formula \( y = a(1 + r)^x \), we get \( y = 2050(1 + 0.02)^x=2050(1.02)^x \).

Answer:

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