Question

Please help!

At the start of 2004, an online social group had 0.6 million members. Since that time, new members joined at a rate of approximately

m(t) = 10.5t2 + 16t − 4 million members per year (0 ≤ t ≤ 3.5)

where t is time in years since the start of 2004.

(a) Find an expression for the total online social group membership M(t) at time t.

M(t) =

(b) Use the answer to part (a) to estimate the group's membership in January 2006. (Round your answer to the nearest million members.)

M(2) = million members

Answer 1

The problem is somewhat ambiguous, because it's not clear if the formula is meant to be evaluated at one year intervals, or represents an instantaneous change in membership at time t, i.e. whether it is \[\Delta M(t)\]or\[\frac{dM}{dt}(t)\]If you are in a calculus class, then probably it's meant to be the latter, so you should integrate the right-hand side (which is a polynomial, simple). Then evaluate at t=2, subtract the value at t=0 (to find delta M), then add the 0.6 million members you had in January 2004.

Answer 2

so set the equation =0 to get part a? and then plug in 2 into that equation for part b?

Answer 3

M (t ) = ∫ m (t) dt
= ∫ ( 10.5t² + 16t − 4 ) dt
= ...
In 2004, M (0) = C = .6 mil
In 2006, M (2) = 3.5 * 8 + 8 * 4 - 4 + .6
= ...

Answer 4

Thankyou all for your responses and help!

Answer 5

Do you still need further explanation?

Answer 6

No I got it from this! Thanks :)