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The function f(t)=Ne(−kt) can be used to model half-life decay, where N is the initial amount, t is time in days and k is a constant. A substance has a k value of 0.328. If the amount of the substance remaining after 14 days is 50 grams, what was the initial amount? Round your answer to the nearest gram, and do not include units.

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JeanaShupp

Answer: 4935 grams.

Step-by-step explanation:

Given, The function [tex]f(t)=Ne^{-kt}[/tex]can be used to model half-life decay, where N is the initial amount, t is time in days and k is a constant.

A substance has a k value of 0.328.

i.e. k= 0.328

The amount of the substance remaining after 14 days is 50 grams, i.e. put t= 14 and f(t) = 50 in the above equation, we get

[tex]50=Ne^{-(0.328)\times14}\\\\\Rightarrow\ 50=Ne^{-4.592}\\\\\Rightarrow\ 50=N(0.0101325729488)\\\\\Rightarrow\ N=\dfrac{50}{0.0101325729488}\\\\\Rightarrow\ N=4934.58080713\approx 4935\ grams[/tex]

Hence, the initial amount was 4935 grams.

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