the mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. a…

the mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. a sample increases continuously at a relative rate of 3% per day. find the mass of the sample after four days if there were 17 grams of the substance present at the beginning of the study. do not round any intermediate computations, and round your answer to the nearest tenth.

the mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. a sample increases continuously at a relative rate of 3% per day. find the mass of the sample after four days if there were 17 grams of the substance present at the beginning of the study. do not round any intermediate computations, and round your answer to the nearest tenth.

Answer

Explanation:

Step1: Identificar la fórmula de crecimiento exponencial continuo

La fórmula es $A = A_0e^{rt}$, donde $A_0$ es la cantidad inicial, $r$ es la tasa de crecimiento y $t$ es el tiempo.

Step2: Asignar valores a las variables

Tenemos $A_0 = 17$ gramos, $r=0.03$ (3% expresado como decimal) y $t = 4$ días.

Step3: Sustituir valores en la fórmula

$A=17e^{0.03\times4}$.

Step4: Calcular el valor de $A$

$A = 17e^{0.12}$. Usando una calculadora, $e^{0.12}\approx1.127497$, entonces $A = 17\times1.127497\approx19.2$.

Answer:

$19.2$ gramos