Carbon-14 is an element that loses about 10% of its mass every millennium (i.e., 1000 years). A sample of Carbon-14 has 600 grams. Write a function that gives the sample's mass in grams, S(t),t millennia from today. S(t)=

Exponential Decay Function: Step 1: To model the decay of Carbon-14, we use an exponential decay function. The general form of an exponential decay function is S(t) = S_0 * (1 - r)^t, where S_0 is the initial amount, r is the decay rate per time period, and t is the number of time periods. In this case, S_0 is 600 grams, r is 10% or 0.10, and t is the number of millennia. Substitute Values: Step 2: Substitute the given values into the exponential decay function. We get S(t) = 600 * (1 - 0.10)^t. This simplifies to S(t) = 600 * (0.90)^t, since 1 - 0.10 = 0.90. Final Mass Calculation: Step 3: The function S(t) = 600 * (0.90)^t now represents the mass of the Carbon-14 sample in grams, t millennia from today.

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Carbon-14 is an element that loses about
10% of its mass every millennium (i.e., 1000 years). A sample of Carbon-14 has 600 grams.
Write a function that gives the sample's mass in grams,
S(t),t millennia from today.

S(t)=

Carbon $-14$ is an element that loses about $10 \%$ of its mass every millennium (i.e., $1000$ years). A sample of Carbon $-14$ has $600$ grams. $\newline$ Write a function that gives the sample's mass in grams, $S(t), t$ millennia from today. $\newline$ $S(t)=\square$

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Q. Carbon

-14

is an element that loses about

10 \%

of its mass every millennium (i.e.,

1000

years). A sample of Carbon

-14

has

600

grams.

\newline

Write a function that gives the sample's mass in grams,

S(t), t

millennia from today.

\newline

S(t)=\square

Exponential Decay Function: Step $1$ : To model the decay of Carbon $-14$ , we use an exponential decay function. The general form of an exponential decay function is $S(t) = S_0 \times (1 - r)^t$ , where $S_0$ is the initial amount, $r$ is the decay rate per time period, and $t$ is the number of time periods. In this case, $S_0$ is $600$ grams, $r$ is $10\%$ or $0.10$ , and $t$ is the number of millennia.
Substitute Values: Step $2$ : Substitute the given values into the exponential decay function. We get $S(t) = 600 \times (1 - 0.10)^t$ . This simplifies to $S(t) = 600 \times (0.90)^t$ , since $1 - 0.10 = 0.90$ .
Final Mass Calculation: Step $3$ : The function $S(t) = 600 \times (0.90)^t$ now represents the mass of the Carbon $-14$ sample in grams, $t$ millennia from today.