Answer:
500 copies per year after 6 months
Explanation:
Equation for circulation :
C(t) =100t² + 400t + 5000
To find the rate of increase in circulation, namely the tangent to the equation, take the first derivative C'(t)
[tex]C'(t) = \dfrac{d}{dt}\left(100t^2+400t+5000\right)\\= \dfrac{d}{dt}\left(100t^2\right)+\dfrac{d}{dt}\left(400t\right)+\dfrac{d}{dt}\left(5000\right)[/tex]
[tex]\dfrac{d}{dt}\left(100t^2\right)=200t\\\\\dfrac{d}{dt}\left(400t\right)=400\\\\\dfrac{d}{dt}\left(5000\right)=0[/tex]
[tex]C'(t) =200t + 400[/tex]
In six months which corresponds to 0.5 year, we can find C'(0.5) by substituting 0.5 in the expression
[tex]C'(0.5) = 200 \cdot 0.5 + 400 = 100 + 400\\\\[/tex]
[tex]= 500[/tex] copies per year
