Can someome please show me how to setup & solve these problems in detail please?

Question

Can someome please show me how to setup & solve these problems in detail please?
Thank you!

of bacteria can be modeled 4. The amount of radioactive isotope !"C can be used to as continuous exponential growth. The sample is first taken with 125 cells. After 12 hours, the sample has 280 cells. Determine the time it takes for the sample to reach 500 cells determine the age of a fossil. After 5,730 years, half of the isotope C will remain, the rest decays (exponentially and continuously). Determine the age of a fossil that contains 32% of its original amount of

Explanation / Answer

3) initial value of samples = 125

after 12 hours = 280 cells

so we can write the function

280 = 125 e^(k*12)

280 / 125 = e^(12k)

k = ln ( 280 / 125 ) / 12

k = 0.0672

hence, function becomes

P = 125 e^.0672t

plugging P = 500

500 = 125 e^.0672t

500 / 125 =  e^.0672t

t = ln ( 500 / 125 ) / .0672

t = 20.63 hours

it takes 20.63 hours to reach 500 cells

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