NJSLA Mathematical Reasoning and Modeling 2

Question 1

A town's population grows according to the model P(t) = 12,000 · (1.03)^t, where t is years. What does the value 1.03 represent?

Accepted Answer

A 3% annual growth rate

Answer

In an exponential growth model P = P₀ · b^t, the base b = 1.03 means the population increases by 3% each year.

Question 2

A rectangle has a perimeter of 54 cm and a length that is twice its width. Which equation correctly models this situation?

Accepted Answer

2w + 2(2w) = 54

Answer

Perimeter = 2(length + width) = 2(2w + w) = 6w = 54, so the equation 2w + 2(2w) = 54 correctly models the perimeter.

Question 3

On a number line, which value is closest to √50?

Accepted Answer

7

Answer

Since 7² = 49 and 8² = 64, √50 ≈ 7.07, making 7 the closest whole number.

Question 4

A car rental company charges $40 per day plus $0.15 per mile. Which inequality represents renting for 3 days and staying under $200?

Accepted Answer

120 + 0.15m ≤ 200

Answer

The cost for 3 days is 3 × $40 = $120 plus $0.15 per mile, giving 120 + 0.15m ≤ 200 for staying within budget.

Question 5

A function is defined as f(x) = 3x² − 12. For which value of x does f(x) = 0?

Accepted Answer

x = ±2

Answer

Setting 3x² − 12 = 0 gives x² = 4, so x = ±2.

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