An element with a mass of 540 grams decays by 17.9% per minute to the nearest tenth of a minute how long will it be until there are 90 grams of the element remainibg

It'll take approximately 9.1 minutes

Step-by-step explanation:

The decay of this element can be modeled by the following expression:

m(t) = 540*(1 - 0.179)^t

Where m is the mass of the element in a given minute t. This expression comes from a compounded interest formula, with negative rate, since they will work in the same manner. Therefore to find how long until it reaches 90 g, we need to make m = 90 and solve for t.

90 = 540*(0.821)^t

(0.821)^t = 90 / 540

(0.821)^t = 1/6

ln(0.821^t) = ln(1/6)

t*ln(0.821) = ln(1) - ln(6)

t*ln(0.821) = - ln(6)

t = -ln(6)/ln(0.821) = 9.08452

It'll take approximately 9.1 minutes

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