Question

question 39 of 40
rosa recorded the height (in centimeters) of a pea plant over a 10 - day period for a science experiment. which equation is the best model of the data?

a. ( y = 20cdot(1.4^{x}) )
b. ( y = 0.5x + 1.8 )
c. ( y = 22cdot(1.1^{x}) )
d. ( y = 0.7x + 2.1 )

Explanation:

Step1: Analyze the data trend

The data shows a linear - like trend (not an exponential trend as exponential functions grow much faster). So we can eliminate options A and C (which are exponential functions \(y = a\cdot b^{x}\)).

Step2: Test option B

For \(y = 0.5x+1.8\):
When \(x = 1\), \(y=0.5\times1 + 1.8=0.5 + 1.8 = 2.3\) (close to the actual \(y = 2\)).
When \(x = 2\), \(y=0.5\times2+1.8 = 1 + 1.8=2.8\) (close to the actual \(y = 3\)).
When \(x = 3\), \(y=0.5\times3+1.8=1.5 + 1.8 = 3.3\) (close to the actual \(y = 3\)).
When \(x = 4\), \(y=0.5\times4+1.8=2 + 1.8 = 3.8\) (close to the actual \(y = 4\)).
When \(x = 5\), \(y=0.5\times5+1.8=2.5 + 1.8=4.3\) (close to the actual \(y = 4.5\)).
When \(x = 6\), \(y=0.5\times6+1.8=3 + 1.8 = 4.8\) (close to the actual \(y = 5\)).
When \(x = 7\), \(y=0.5\times7+1.8=3.5 + 1.8=5.3\) (close to the actual \(y = 5\)).
When \(x = 8\), \(y=0.5\times8+1.8=4 + 1.8 = 5.8\) (close to the actual \(y = 6\)).
When \(x = 9\), \(y=0.5\times9+1.8=4.5 + 1.8=6.3\) (close to the actual \(y = 6.5\)).
When \(x = 10\), \(y=0.5\times10+1.8=5 + 1.8 = 6.8\) (close to the actual \(y = 6.5\)).

Step3: Test option D

For \(y = 0.7x+2.1\):
When \(x = 1\), \(y=0.7\times1+2.1=0.7 + 2.1=2.8\) (not as close to \(y = 2\) as option B).
When \(x = 2\), \(y=0.7\times2+2.1 = 1.4+2.1=3.5\) (not as close to \(y = 3\) as option B).

Answer:

B. \(y = 0.5x+1.8\)