Question

1. remember: $y = a(1pm r)^x$ at the beginning of the black plague the spread of the virus occurred rapidly. it was spreading at a rate of 5.23% per day. how long would it take to double if initially 49 people had it? (round to the nearest whole day.)

Explanation:

Step1: Identificar los valores iniciales

Tenemos $a = 49$, $r=0.0523$ y queremos que $y = 2\times49 = 98$. La fórmula es $y=a(1 + r)^x$.

Step2: Sustituir valores en la fórmula

Sustituyendo obtenemos $98 = 49(1 + 0.0523)^x$.

Step3: Simplificar la ecuación

Dividimos ambos lados de la ecuación por 49: $\frac{98}{49}=(1.0523)^x$, es decir $2=(1.0523)^x$.

Step4: Aplicar logaritmo

Tomamos logaritmo en ambos lados: $\log(2)=\log(1.0523^x)$.

Step5: Aplicar propiedad de logaritmos

Usando la propiedad $\log(a^b)=b\log(a)$ tenemos $\log(2)=x\log(1.0523)$.

Step6: Resolver para x

Despejamos $x$: $x=\frac{\log(2)}{\log(1.0523)}$.

Step7: Calcular el valor de x

$x=\frac{0.30103}{0.02207}\approx14$.

Answer:

14