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)= ◻

Convert to decimal: Convert the percentage loss to a decimal. 10% as a decimal is 10/100 = 0.1.Determine decay factor: Determine the decay factor for the function. Since the sample loses mass, the decay factor (b) is 1 minus the decimal loss. b = 1 - 0.1 = 0.9.Write exponential decay function: Write the exponential decay function using the initial mass and the decay factor. Initial mass (a) = 600 grams. Decay factor (b) = 0.9. The function is S(t) = 600(0.9)^t, where t is the number of millennia.

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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. $\newline$ $S(t)=$ $\newline$ $\square$

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Algebra 2

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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)=

\newline

\square

Convert to decimal: Convert the percentage loss to a decimal. $\newline$ $10\%$ as a decimal is $\frac{10}{100} = 0.1$ .
Determine decay factor: Determine the decay factor for the function. $\newline$ Since the sample loses mass, the decay factor $b$ is $1$ minus the decimal loss. $\newline$ $b = 1 - 0.1 = 0.9$ .
Write exponential decay function: Write the exponential decay function using the initial mass and the decay factor. $\newline$ Initial mass $a$ = $600$ grams. $\newline$ Decay factor $b$ = $0.9$ . $\newline$ The function is $S(t) = 600(0.9)^t$ , where $t$ is the number of millennia.