Suppose that w and t vary inversely and that t = 1/5 when w = 4. Write a function that models the inverse variation, and find t when w = 9.

Question

(1 point)
Responses

a t=1/5w; 4/45
b t=1/5w; 1/5
c t=1/20w; 1/80
d t=4/5w; 4/45

Answer 1

a t=1/5w; 4/45

To find the function that models the inverse variation, we know that t = k/w, where k is a constant of variation.

Given that t = 1/5 when w = 4:
1/5 = k/4
k = 4/5

Therefore, the function that models the inverse variation is t = (4/5)/w = 4/5w.

Now, to find t when w = 9:
t = 4/5 * 9 = 36/5 = 7 1/5 = 7.2

So, t = 7.2.