Final Answer:
It will take the young sumo wrestler approximately 52.8 months to reach a weight of 350 pounds.
Step-by-step explanation:
The given equation
�
=
80
+
5.4
�
W=80+5.4t represents the model for the wrestler's weight, where
�
W is the weight in kilograms, and
�
t is the time in months. The goal is to find the time (
�
t) it takes for the wrestler to reach a weight of 350 pounds. First, we convert 350 pounds to kilograms using the conversion unit
1
pound
=
0.454
kg
1 pound=0.454 kg, yielding
350
pounds
×
0.454
kg/pound
≈
158.9
kg
350 pounds×0.454 kg/pound≈158.9 kg.
Now, we substitute
�
=
158.9
kg
W=158.9 kg into the equation and solve for
�
t:
158.9
=
80
+
5.4
�
158.9=80+5.4t
5.4
�
=
158.9
−
80
5.4t=158.9−80
5.4
�
=
78.9
5.4t=78.9
�
≈
78.9
5.4
≈
14.61
months
t≈
5.4
78.9
≈14.61 months
Therefore, it will take the young sumo wrestler approximately 14.61 months to reach a weight of 350 pounds. It's important to note that this is an approximation, and in practical terms, the wrestler may round up to the nearest whole number of months, so the final answer is approximately 15 months.
Understanding and applying mathematical models, such as the given equation, allows us to make predictions and solve real-world problems. In this case, the model helps estimate the time required for the sumo wrestler to achieve a specific weight goal.