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Nataly_w [17]
2 years ago
15

A palindrome is a number that reads the same forwards and backwards, such as 22 or 39793.

Mathematics
1 answer:
Aleks04 [339]2 years ago
5 0

Answer:

There are thirty-nine palindromic numbers between 10 and 400.

Step-by-step explanation:

Listed, they are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, and 393.

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Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14
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Answer:

<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

N(t)=N_{0}e^{-\lambda t}

Where:

No  = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

\lambda     = The decay constant.

One important parameter related to radioactive decay is the half-life:

\displaystyle t_{1/2}=\frac {\ln(2)}{\lambda }

If we know the value of the half-life, we can calculate the decay constant:

\displaystyle \lambda=\frac {\ln(2)}{ t_{1/2}}

Carbon-14 has a half-life of 5,730 years, thus:

\displaystyle \lambda=\frac {\ln(2)}{ 5,730}

\lambda=0.00012097

The equation of the remaining quantity of Carbon-14 is:

N(t)=N_{0}e^{-0.00012097\cdot t}

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

0.10N_o=N_{0}e^{-0.00012097\cdot t}

Simplifying:

0.10=e^{-0.00012097\cdot t}

Taking logarithms:

ln 0.10=-0.00012097\cdot t

Solving for t:

\displaystyle t=\frac{log 0.10}{-0.00012097}

t\approx 19,035\ years

Carbon-14 will take 19,035 years to decay to 10 percent.

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