Question

Timmy is building a new website. Right after he starts, he has 2 visitors. He expects his visitors to increase according to a model he developed for his other websites growth, v(t)=10t+b, where b is the number of visitors right afte he starts building his website, t is the time since he stgarted building his website in weeks and v(t) is the nunber of total visitors after t weeks.

How many visitors does he get 4 weeks after starting to build his website?

How any new visitors does he get per week?

Answer 1

He gets 42 visitors 4 weeks after starting to build his website.

He gets 10 new visitors per week.

Explanation:

Equation for the number of visitors:

The equation for the number of visitors Timmy's new website receives after t weeks is:

`v(t) = 10t + b`

In which b is the number of visitors rightly after he starts.

Timmy is building a new website. Right after he starts, he has 2 visitors.

This means that
`b = 2`, so:

`v(t) = 10t + 2`

How many visitors does he get 4 weeks after starting to build his website?

This is v(4). So

`v(4) = 10(4) + 2 = 40 + 2 = 42`

He gets 42 visitors 4 weeks after starting to build his website.

How any new visitors does he get per week?

After 0 weeks:

`v(0) = 10(0) + 2 = 0 + 2 = 2`

After 1 week:

`v(1) = 10(1) + 2 = 10 + 2 = 12`

2 weeks:

After 2 week:

`v(2) = 10(2) + 2 = 20 + 2 = 22`

22 - 12 = 12 - 2 = 10

He gets 10 new visitors per week.