the radioactive substance uranium - 240 has a half - life of 14 hours. the amount a(t) of a sample of…

the radioactive substance uranium - 240 has a half - life of 14 hours. the amount a(t) of a sample of uranium - 240 remaining (in grams) after t hours is given by the following exponential function. a(t)=4700(1/2)^(t/14) find the initial amount in the sample and the amount remaining after 50 hours. round your answers to the nearest gram as necessary. initial amount: grams amount after 50 hours: grams

the radioactive substance uranium - 240 has a half - life of 14 hours. the amount a(t) of a sample of uranium - 240 remaining (in grams) after t hours is given by the following exponential function. a(t)=4700(1/2)^(t/14) find the initial amount in the sample and the amount remaining after 50 hours. round your answers to the nearest gram as necessary. initial amount: grams amount after 50 hours: grams

Answer

Explicación:

Paso 1: Encontrar la cantidad inicial

Para encontrar la cantidad inicial, sustituimos (t = 0) en la función (A(t)=4700\left(\frac{1}{2}\right)^{\frac{t}{14}}). $$A(0)=4700\left(\frac{1}{2}\right)^{\frac{0}{14}}=4700\left(\frac{1}{2}\right)^0$$ Como cualquier número (excepto 0) elevado a la potencia 0 es 1, entonces (A(0) = 4700).

Paso 2: Encontrar la cantidad después de 50 horas

Sustituimos (t = 50) en la función (A(t)=4700\left(\frac{1}{2}\right)^{\frac{t}{14}}). $$A(50)=4700\left(\frac{1}{2}\right)^{\frac{50}{14}}=4700\left(\frac{1}{2}\right)^{\frac{25}{7}}$$ Calculamos (\left(\frac{1}{2}\right)^{\frac{25}{7}}\approx0.057). Luego (A(50)=4700\times0.057\approx268).

Respuesta:

Initial amount: 4700 grams Amount after 50 hours: 268 grams