Answer: Linear model [tex]H(t)=9t+100[/tex] and H'(t) = 9 units.
Step-by-step explanation:
Since we have given that
In 2000, amount spent = $100 billions
In 2010, amount spent = $190 billions.
So, rate of increase would be
[tex]\dfrac{190-100}{2010-2000}\\\\=\dfrac{90}{10}\\\\=9[/tex]
So, linear model for H(t) would be
[tex]H(t)-190=9(t-10)\\\\H(t)=9t-90+190\\\\H(t)=9t+100[/tex]
So, H'(t) would be 9.
Hence, linear model [tex]H(t)=9t+100[/tex] and H'(t) = 9 units.