I really need help with a math word problem..

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The function A = A0e-0.01155x models the amount in pounds of a particular radioactive material stored in a concrete vault, where A0is the original amount of material and x is the number of years since the material was put in the vault.  If 900 pounds of material are placed in the vauld, how much time will need to pass for only 357 pounds to remain?

Apr 16th, 2015

Ao = 900 

A = 357

Substitute those values into the equation and solve for x = time

357 = 900e^-0.01155x

357/900 = e^-0.01155x

119/300 = e^-0.01155x

Undo the base of an exponent by multiplying it by the log of the base

log(e)(119/300) = -0.01155x

x = log(e)(119/300)/.-0.01155

x = 14.92 years

Apr 16th, 2015

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Apr 16th, 2015
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Apr 16th, 2015
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