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The number y of hits a new website receives each month can be modeled by
y = 4090ekt,
where t represents the number of months the website has been operating. In the website's third month, there were 10,000 hits. Find the value of k. (Round your answer to four decimal places.)

Respuesta :

Answer:

k = 0.2980

Step-by-step explanation:

Given:

number of months t =3

number of hits y = 10000

The equation is modeled as

[tex]y= 4090e^{kt}[/tex]

We need to find value of k.

Now Substituting the values in above equation we get.

[tex]10000= 4090e^3k\\e^{3k}=\frac{10000}{4090}\\\\[/tex]

Now taking Anti log on both side to remove e we get,

[tex]3k = \ ln \frac{10000}{4090}\\\\3k = 0.8940\\k = \frac{0.8940}{3}= 0.2980[/tex]

Hence the value of k = 0.2980.

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