Liam's pumpkin will weigh more in week 10, and Patricia's pumpkin will weigh more in week 13. Then the correct option is C.
What is the linear system?
A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The table below shows the weights of Liam's pumpkin, l(w), and Patricia's pumpkin, p(w), over a four-week period which represents the number of weeks.
Liam's pumpkin grows at a constant rate.
Patricia's pumpkin grows at a weekly rate of approximately 52%.
Let x be the number of the week and y be the weight in pounds.
The equation of Liam's pumpkin will be
[tex]\rm y - 2.4 = \dfrac{5.5-2.4}{7-6} (x- 6)\\\\y - 2.4 = 3.1(x- 6)\\\\y = 3.1x - 16.2[/tex]
Then the weight of Liam's pumpkin after 10 weeks will be
y = 3.1 × 10 - 16.2
y = 31 - 16.2
y = 14.8
Then the weight of Liam's pumpkin after 10 weeks will be
y = 3.1 × 13 - 16.2
y = 40.3 - 16.2
y = 24.1
The equation of Patricia's pumpkin will be
[tex]\rm y = a\times (1.52)^{x}[/tex]
For x = 6 and y = 2.5
Then
[tex]\rm 2.5 = a \times 1.52^6\\\\a \ \ = 0.203[/tex]
We have
[tex]\rm y = 0.203 \times (1.52)^{x}[/tex]
Then the weight of Patricia's pumpkin after 10 weeks will be
[tex]\rm y = 0.203 \times (1.52)^{10}\\\\y = 13.36[/tex]
Then the weight of Patricia's pumpkin after 13 weeks will be
[tex]\rm y = 0.203 \times (1.52)^{13}\\\\y = 46.93[/tex]
More about the linear system link is given below.
https://brainly.com/question/20379472
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