Question

1 the population growth of boomtown is shown in the accompanying graph.
if the same pattern of population growth continues, what will the population of boomtown be in the year 2020?

1. 20,000 3) 40,000
2. 32,000 4) 64,000

Explanation:

Step1: Analyze the pattern

From the table, when \(x = 0\) (corresponding to 1980), \(y=2\) (in thousands); when \(x = 10\) (1990), \(y = 4\); when \(x=20\) (2000), \(y = 8\); when \(x = 30\) (2010), \(y=16\). We can observe that the population \(y\) (in thousands) follows the pattern \(y = 2^{x/10 + 1}\).

Step2: Calculate for \(x = 40\) (2020)

Substitute \(x = 40\) into the formula \(y=2^{x/10 + 1}\).

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Answer:

1. \(32,000\)