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]
