Since p is inversely proportional to t, the table of values should be completed as follows;
t 100 25 20 50
p 1 4 5 2
In Mathematics, an inverse variation can be modeled or represented by this mathematical expression:
p ∝ 1/t
p = k/t
Where:
- p represents the p-variable.
- t represents the t-variable.
- k represents the constant of proportionality.
Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:
k = pt
k = 100
When t is 25, the value of p is given by;
p = k/t
p = 100/25
p = 4.
When p is 5, the value of t is given by;
t = k/p
t = 100/5
t = 20
When t is 2, the value of p is given by;
p = 100/2
p = 50.