Having high blood pressure for a long time can increase your risk of heart disease (R). For this problem, we will use (T) to denote the total length of time someone has had high blood pressure over the course of their life (this is different from our normal time variable!). Assume that when a person has had high blood pressure for 5 years, they currently have a 5% chance of developing heart disease at some point and dR/dT = 0.5. When a person has had high blood pressure for 10 years, assume their current risk of heart disease is 15%, and that dR/dT = 5.

a) Explain (without using the term "derivative") what the quantity dR/dT represents in this case.

b)In this scenario, will the risk of heart disease increase more per year for someone who has had high blood pressure for 5 years or for someone who has had high blood pressure for 10 years? Explain.

c) Write the equation of a tangent line for someone who has had high blood pressure for 5 years, and use this equation to predict their risk of heart disease after they have had high blood pressure for 10 years.

d) Why does the answer you got in part (c) not match the risk at 10 years given at the start of the problem? What does this tell you about the shape of the function R(T)?