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Oh no! The zombie virus that began with Mr. Smith has now been passed on to students! Suppose the new virus infected 10 students all at once. Then, each newly-turned zombie infects exactly 3 other people, so that the zombie population triples every day. The formula to model this situation is P = 10(3)x

a) On what day will there be a zombie population over 2,000? Explain how you found this answer.

b) If a cure is not found and the virus continues to spread, how many new zombie will there be on day 10? Explain how you found this answer.

Respuesta :

calculista

Answer:

Part a) In the day 5 will be a zombie population over 2,000

Part b) [tex]590,490\ zombies[/tex]

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

[tex]P=a(1+r)^x[/tex]

where

P is the population of zombie

x is the number of days

a is the initial value

r is the rate of change

we have

[tex]a=10\\r=200\%=200/100=2[/tex]

substitute

[tex]P=10(1+2)^x[/tex]

[tex]P=10(3)^x[/tex]

Part a) On what day will there be a zombie population over 2,000?

For P=2,000

substitute in the exponential equation

[tex]2,000=10(3)^x[/tex]

solve for x

[tex]200=3^x[/tex]

Apply log both sides

[tex]log(200)=xlog(3)[/tex]

[tex]x=log(200)/log(3)[/tex]

[tex]x=4.8\ days[/tex]

therefore

In the day 5 will be a zombie population over 2,000

Part b) If a cure is not found and the virus continues to spread, how many new zombie will there be on day 10?

For x=10 days

substitute in the equation

[tex]P=10(3)^{10}= 590,490\ zombies[/tex]

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