Suppose that y varies directly as x . if y is 24 when x is 6, find the constant of variation and the direct variation equation

Step-by-step explanation:

Direct variation can be modeled by y = kx where k is the constant of variation!

So to solve for k all we need to do is substitute in the value for y and x that are given.

So according to the problem y = 24 when x = 6

24 = 6k

Divide both sides by 6

k = 4

So the constant of variation is 4

The direct variation equation would then be

y = 4x

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

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step-by-step explanation: