Answer:
Step-by-step explanation:
[tex]P(t)=50001+Be^{-kt}[/tex]
If t is years since January 1, 2010, then on January 1, 2010, t = 0.
On April 1, 2010, there are 3 months from January 1, 2010. t = 0.25 (3 months ÷ 12 months)
At t = 0, P(t) = 500
[tex]P(0)=500 = 50001+Be^{-k\times0} = 50001+B[/tex]
[tex]B = 500 - 50001 = -49501[/tex]
At t = 0.25, P(t) = 750
[tex]P(0)=750 = 50001-49501e^{-k\times0.25}[/tex]
[tex]49501e^{-0.25k} = 50001[/tex]
[tex]e^{-0.25k} =\dfrac{50001}{49501} = 1.0101[/tex]
[tex]-0.25k = \ln1.0101 = 0.01[/tex]
[tex]k = -\dfrac{0.01}{0.25} = -0.04[/tex]
Substituting for B and k in P(t),
[tex]P(t)=50001-49501e^{-0,04t}[/tex]
