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Andrea conducts a science experiment and observes that the height of a plant depends on the amount of sunlight it receives. The plant's height is 37 centimeters, and it grows at a rate of 0.004 centimeters per hour of sunlight. If the number of hours of sunlight is represented by the variable [tex][tex]$s$[/tex][/tex], which function can represent the height of the plant?

A. [tex]s(h) = 0.004 h - 37[/tex]
B. [tex]f(h) = 37 h + 0.004[/tex]
C. [tex]f(s) = 0.004 s + 37[/tex]

Sagot :

GinnyAnswer
To determine the function that represents the height of the plant based on the amount of sunlight it receives, we need to incorporate the given information into a mathematical model.

1. Initial Height: We know the initial height of the plant is 37 centimeters, regardless of the exposure to sunlight. This initial height serves as our constant term in the function.

2. Growth Rate: The plant grows at a rate of 0.004 centimeters per hour of sunlight. This rate is our coefficient for the variable representing the number of hours of sunlight, [tex]\(s\)[/tex].

Combining these points, we construct the function step by step:

- The total height of the plant after receiving [tex]\(s\)[/tex] hours of sunlight is its initial height plus the additional height gained due to sunlight exposure.
- The additional height gained is [tex]\(0.004\)[/tex] centimeters per hour of sunlight, thus over [tex]\(s\)[/tex] hours, the plant gains [tex]\(0.004s\)[/tex] centimeters.
- Therefore, the total height of the plant is the sum of its initial height (37 cm) and the height gained [tex]\(0.004s\)[/tex].

Putting this into a function, we have:
[tex]\[ f(s) = 0.004s + 37 \][/tex]

So, the correct function that represents the height of the plant based on the number of hours of sunlight it receives is:
[tex]\[ f(s) = 0.004s + 37 \][/tex]

Thus, the correct option is:
[tex]\[ f(s) = 0.004s + 37 \][/tex]
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