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2 years ago

5

The amount of a radioactive isotope decays in half every year. The amount of the isotope can be modeled by f(x) = 346(one half)x

and f(1) = 173. What does the one half represent?

1 answer:

Leno4ka [110]2 years ago

8 0

It means the first iteration of decay would be 1/2 of 346, which is 173

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$A = A_ob^t$
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Now we solve for b
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$\frac{3600}{3000} = \frac{3000b^{4}}{3000}$
$\frac{6}{5} = b^4$
$\sqrt[4]{\frac{6}{5}} = \sqrt[4]{b^4}$
$\sqrt[4]{\frac{6}{5}} = b$

Now that we have found b, we can use the equation $A = 3000b^t$ to predict how many bacteria will be present after 10 hours.
$b = \sqrt[4]{\frac{6}{5}}$
t = 10
$A = 3000b^t$
$A = 3000\sqrt[4]{\frac{6}{5}}^{10} = 4732.3228 = 4732$

Answer = 4732

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