A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the system

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A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the system

by VJesus12 » Tue Sep 15, 2020 5:33 am

00:00

A

B

C

D

E

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A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the system, only half of them survive every hour. If we start with $$x$$ number of virus and after the $$8$$ hours there are $$2^{40}$$ viruses, what is the value of $$x?$$

A. $$2^{16}$$
B. $$2^{18}$$
C. $$2^{21}$$
D. $$2^{23}$$
E. $$2^{25}$$

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Re: A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the sy

by deloitte247 » Sat Sep 19, 2020 1:08 pm
Every hour virus increases by 16 times itself due to the antivirus/anti agent present, only half of them survive

Given that initial value = x
per hour, x increases by x * 16 * 1/2 = x * 8
After shows, there are 2^40 viruses because the virus multiplies itself, the growth is exponential so for 8 hours
$$x\cdot\left(8\right)^8=2^{40}$$
$$x\cdot\left(2^3\right)^8=2^{40}$$
$$x\cdot2^{24}=2^{40}$$
$$x=\frac{2^{40}}{2^{24}}$$
$$x=2^{40-24}$$
$$x=2^{16}$$

$$Answer\ =\ A$$

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Re: A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the sy

by Scott@TargetTestPrep » Thu Sep 24, 2020 7:12 am
VJesus12 wrote:
Tue Sep 15, 2020 5:33 am
A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the system, only half of them survive every hour. If we start with $$x$$ number of virus and after the $$8$$ hours there are $$2^{40}$$ viruses, what is the value of $$x?$$

A. $$2^{16}$$
B. $$2^{18}$$
C. $$2^{21}$$
D. $$2^{23}$$
E. $$2^{25}$$

Solution:

If the anti-agent kills half of virus every hour, the virus only multiplies itself 8 times every hour. So if at the start, there are x number of the virus and after 8 hours, there are 2^40 viruses, we can create the equation:

x * 8^8 = 2^40

x * (2^3)^8 = 2^40

x * 2^24 = 2^40

x = 2^16

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

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Re: A virus sample multiplies itself by becoming $$16$$ times itself every hour. But due to anti-agent present in the sy

by gentvenus » Thu Sep 24, 2020 11:38 am
x = 2 ^ 16

A

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