5. annual sales for a restaurant were $575,000 in 2006. since then, the sales increased at a rate of 3% per…

5. annual sales for a restaurant were $575,000 in 2006. since then, the sales increased at a rate of 3% per year. write and use an exponential model to find the sales in 2018.

5. annual sales for a restaurant were $575,000 in 2006. since then, the sales increased at a rate of 3% per year. write and use an exponential model to find the sales in 2018.

Answer

Explicación:

Paso 1: Definir el modelo exponencial

El modelo de crecimiento exponencial es $A = P(1 + r)^t$, donde:

  • $P = 575000$ (ventas iniciales),
  • $r = 0.03$ (tasa de crecimiento anual),
  • $t$ = años transcurridos desde 2006.

Paso 2: Calcular el valor de $t$

Calcular los años entre 2006 y 2018: $t = 2018 - 2006 = 12$

Paso 3: Sustituir valores en el modelo

Sustituir $P$, $r$ y $t$ en la fórmula: $A = 575000(1 + 0.03)^{12}$

Paso 4: Calcular el factor de crecimiento

Calcular $(1.03)^{12} \approx 1.42576$

Paso 5: Calcular las ventas finales

Multiplicar el valor inicial por el factor de crecimiento: $A = 575000 \times 1.42576$

Respuesta:

Las ventas en 2018 son aproximadamente $$819,812$