the function $y = 100(0.5)^{\frac{x}{4}}$ models the percent, $y$, of an initial dose of medicine remaining…

the function $y = 100(0.5)^{\frac{x}{4}}$ models the percent, $y$, of an initial dose of medicine remaining in a patients bloodstream after $x$ hours. based on the model, what percent of the initial amount of medicine will remain in the patients bloodstream after 10 hours? round to the nearest whole percent.

the function $y = 100(0.5)^{\frac{x}{4}}$ models the percent, $y$, of an initial dose of medicine remaining in a patients bloodstream after $x$ hours. based on the model, what percent of the initial amount of medicine will remain in the patients bloodstream after 10 hours? round to the nearest whole percent.

Answer

Explanation:

Step1: Sustituir el valor de x

Sustituimos (x = 10) en la función (y = 100(0.5)^{\frac{x}{4}}). [y = 100(0.5)^{\frac{10}{4}}]

Step2: Simplificar el exponente

(\frac{10}{4}=\frac{5}{2}), entonces (y = 100(0.5)^{\frac{5}{2}}).

Step3: Calcular ((0.5)^{\frac{5}{2}})

((0.5)^{\frac{5}{2}}=\sqrt{(0.5)^{5}}=\sqrt{0.03125}\approx0.176777).

Step4: Calcular el valor de y

(y = 100\times0.176777 = 17.6777).

Step5: Redondear al porcentaje entero más cercano

Redondeando (17.6777) al entero más cercano, obtenemos (18).

Answer:

(18)