Progress: Element X decays radioactively with a half life of 5 minutes. If there are 520 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 92 grams?
y = a(.5)

9514 1404 393

  2.5 minutes

Step-by-step explanation:

The amount remaining (y) in grams is given by the exponential function ...

  y = 520(.5^t)

We want to find t when y = 92.

  92 = 520(0.5^t)

  92/520 = 0.5^t

  log(92/520) = t·log(0.5)

  t = log(92/520)/log(0.5) ≈ 2.499 ≈ 2.5

It would take 2.5 minutes for the 520 gram sample to decay to 92 grams.

f

step-by-step explanation:

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answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.