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An epidemic has hit Hanthaway City. The population is declining 24% every hour. In just 8 hours, there are only 15,542 people left in the city. What was the initial population in the city before the epidemic broke out? A)298,406 B)106,011 C)16,298 D)114,389

Respuesta :

mergl
B.) 106, 011 is the closest of these values

Answer:

B) 106,011

Step-by-step explanation:

Since, the population after decaying continuously is,

[tex]A=Pe^{-rt}[/tex]

Where, r is the annual rate of decaying ( in decimals )

t is the number of periods ( in a year )

Here, r = 24 % = 0.24,

t = 8 months,

A = 15,542,

[tex]15542=Pe^{-0.24\times 8}[/tex]

[tex]15542=Pe^{-1.92}[/tex]

[tex]\implies P = \frac{15542}{e^{-1.92}}=106011.33653\approx 106011[/tex]

Hence, the initial population of the city is 106011 ( approx )

Option B is correct.

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