QuestionJune 13, 2025

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=11e^-0.014t where m(t) is measured in kilograms. (a) Find the mass at time t=0 square kg (b) How much of the mass remains after 42 days? (Round your answer to one decimal place.) square kg

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=11e^-0.014t where m(t) is measured in kilograms. (a) Find the mass at time t=0 square kg (b) How much of the mass remains after 42 days? (Round your answer to one decimal place.) square kg
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=11e^-0.014t where m(t) is measured in kilograms. (a) Find the mass at time t=0 square kg (b) How much of the mass remains after 42 days? (Round your answer to one decimal place.) square kg

Solution
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Answer

(a) 11 kg ### (b) 6.7 kg Explanation 1. Calculate the mass at time t=0 Substitute t=0 into the function m(t)=11e^{-0.014t}. This gives m(0) = 11e^{0} = 11 \text{ kg}. 2. Calculate the mass after 42 days Substitute t=42 into the function m(t)=11e^{-0.014t}. Compute m(42) = 11e^{-0.014 \times 42}. Simplify to get m(42) = 11e^{-0.588}. Calculate this value to one decimal place.

Explanation

1. Calculate the mass at time $t=0$<br /> Substitute $t=0$ into the function $m(t)=11e^{-0.014t}$. This gives $m(0) = 11e^{0} = 11 \text{ kg}$.<br /><br />2. Calculate the mass after 42 days<br /> Substitute $t=42$ into the function $m(t)=11e^{-0.014t}$. Compute $m(42) = 11e^{-0.014 \times 42}$. Simplify to get $m(42) = 11e^{-0.588}$. Calculate this value to one decimal place.
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