Given the details of Andrea's science experiment, let's determine the correct function to represent the height of the plant based on the number of hours of sunlight it receives:
1. Initial Height: The initial height of the plant is 37 centimeters.
2. Growth Rate: The plant grows at a rate of 0.004 centimeters per hour of sunlight.
3. Variable for Sunlight Hours: The number of hours of sunlight is represented by the variable [tex]\( s \)[/tex].
We need to express the height of the plant as a function of the number of hours of sunlight [tex]\( s \)[/tex].
Step-by-Step Solution:
1. Identify the Constant Term:
- The term that represents the initial height of the plant, which remains constant regardless of the hours of sunlight, is 37 centimeters. So, this will be our constant term in the function.
2. Identify the Growth Rate Term:
- The plant grows at a rate of 0.004 centimeters for every hour of sunlight. Since [tex]\( s \)[/tex] represents the number of hours of sunlight, the growth contribution to the height will be [tex]\( 0.004 \times s \)[/tex].
3. Construct the Function:
- To obtain the total height of the plant after [tex]\( s \)[/tex] hours of sunlight, we add the initial height to the growth contribution. Therefore, the height function [tex]\( f(s) \)[/tex] becomes:
[tex]\[
f(s) = \text{initial height} + \text{(growth rate} \times \text{hours of sunlight)}
\][/tex]
4. Substitute the Known Values:
- The initial height is 37 centimeters.
- The growth contribution is [tex]\( 0.004 \times s \)[/tex].
Therefore, the function becomes:
[tex]\[
f(s) = 37 + 0.004 \times s
\][/tex]
5. Simplify and Write the Function:
- The simplified expression for the height of the plant as a function of hours of sunlight [tex]\( s \)[/tex] is:
[tex]\[
f(s) = 0.004s + 37
\][/tex]
Given these steps, 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]
This matches the function [tex]\( f(s)=0.004 s+37 \)[/tex] from the provided options.
