Question

Please help soon!!!!!!

Answer 1

Solving the exponential function, it is found that the times that will take to have the desired measures are given by:

a) 3.6 hours.

b) 38.51 hours.

c) 56.98 hours.

What is the exponential function for the amount of Carbon-10 after t hours?

The function is given by:

$A(t) = 140(0.5)^{\frac{t}{19.255}}$

Solving for t, we have that:

$(0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}$

$\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}$

$\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}$

$t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}$

In item A, we have that A(t) = 123, hence:

$t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}$

t = 3.6 hours.

In item B, we have that A(t) = 35, hence:

$t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}$

t = 38.51 hours.

In item C, we have that A(t) = 18, hence:

$t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}$

t = 56.98 hours.

More can be learned about exponential functions at brainly.com/question/25537936

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