Carbon-14 is an element which loses exactly half of its mass every 5730 years. The mass of a sample of carbon-14 can be modeled by a function, $M$, which depends on its age, $t$ (in years).

We measure that the initial mass of a sample of carbon-14 is 741 grams.
Write a function that models the mass of the carbon-14 sample remaining $t$ years since the initial measurement.
$$
M(t)=
$$
$\square$

Question

Carbon-14 is an element which loses exactly half of its mass every 5730 years. The mass of a sample of carbon-14 can be modeled by a function, $M$, which depends on its age, $t$ (in years).

We measure that the initial mass of a sample of carbon-14 is 741 grams.
Write a function that models the mass of the carbon-14 sample remaining $t$ years since the initial measurement.
$$
M(t)=
$$
$\square$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To model the decay of Carbon-14, we use the exponential decay formula, which is $M(t) = M_0 imes \left(\frac{1}{2} ight)^{\frac{t}{T}}$, where $M_0$ is the initial mass and $T$ is the half-life of the substance. ‖ ‖ step 2 ⋮ Given that the initial mass $M_0$ is 741 grams and the half-life $T$ is 5730 years, we substitute these values into the formula to get $M(t) = 741 imes \left(\frac{1}{2} ight)^{\frac{t}{5730}}$. ‖ ‖ step 3 ⋮ Simplifying the expression, we have $M(t) = 741 imes 0.5^{\frac{t}{5730}}$. This is the function that models the remaining mass of the Carbon-14 sample after $t$ years. ‖ ∻[1] Answer∻ ⚹ $M(t) = 741 imes 0.5^{\frac{t}{5730}}$ ⚹ ∻Key Concept∻ ⚹Exponential Decay⚹ ∻Explanation∻ ⚹The function $M(t) = 741 imes 0.5^{\frac{t}{5730}}$ represents the exponential decay of Carbon-14, where the mass halves every 5730 years.⚹◊What is the general formula to calculate the remaining mass of a radioactive substance undergoing decay after a certain number of years?⍭ Generate me a similar question◊

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