Question

The number y of hits a new website receives each month can be modeled by y = 4070ekt, where t represents the number of months the website has been operating. In the website's third month, there were 9,000 hits. Find the value of k. (Round your answer to four decimal places.)

Answer 1

k = 0.2645

Explanation:

Given model:

y = 4070
`e^(kt)`

y = no. of hits website received = 9000 (in 3rd month)

t= no. of months website has been operational = 3

put in the above equation:

9000 = 4070
`e^(3k)`

`(9000)/(4070)` =
`e^(3k)`

`(900)/(407)`=
`e^(3k)`

Taking natural logarithm on both sides, we get:

`ln(900)/(407)`=
`ln(e^(3k))`

`ln(900)/(407)`= 3k lne

lne=1

`ln (900)/(407)`= 3k

or k =
`(1)/(3)`
`ln(900)/((407))`

k =
`(1)/(3)`(0.7936)

k = 0.2645