Let's analyze the problem and find out how much weight the wrestler gains every 2 months.
The weight [tex]\( w \)[/tex] of the wrestler after [tex]\( t \)[/tex] months on the special diet is represented by the equation:
[tex]\[ w = 80 + 5.4t \][/tex]
Here, [tex]\( w \)[/tex] is the weight of the wrestler in kilograms and [tex]\( t \)[/tex] is the time in months.
The term [tex]\( 5.4t \)[/tex] in the equation tells us that the weight gain is directly proportional to the number of months, [tex]\( t \)[/tex]. This means that for each month the wrestler is on the diet, the wrestler gains 5.4 kilograms.
To find out the weight gain over 2 months, we can multiply the weight gain per month by the number of months:
[tex]\[ \text{Weight gain per month} = 5.4 \, \text{kg/month} \][/tex]
[tex]\[ \text{Number of months} = 2 \][/tex]
Therefore, the weight gain over 2 months is:
[tex]\[ 5.4 \, \text{kg/month} \times 2 \, \text{months} = 10.8 \, \text{kg} \][/tex]
Hence, the wrestler gains [tex]\( 10.8 \)[/tex] kilograms every 2 months.
