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:
[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]
Solving for t, we have that:
[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]
[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]
[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
In item A, we have that A(t) = 123, hence:
[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]
t = 3.6 hours.
In item B, we have that A(t) = 35, hence:
[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]
t = 38.51 hours.
In item C, we have that A(t) = 18, hence:
[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]
t = 56.98 hours.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
