Final answer:
To estimate c(2100), we use a linear approximation based on the given c(2000) value and the rate of change dc/dr. Multiplying dc/dr by the change in r (100 years) and adding it to c(2000) gives us an estimated value of approximately 835 for c(2100).
Step-by-step explanation:
The question seeks an estimated value of a function c(2100) given c(2000) and the rate of change dc/dr at r=2000. To estimate c(2100), we will use a linear approximation which assumes that the rate of change between c(2000) and c(2100) is constant and equal to 0.35. This rate, expressed as the derivative of c with respect to r, is used to predict changes in the function over short intervals.
We calculate c(2100) as follows:
c(2100) ≈ c(2000) + (dc/dr) * Δr
Where:
- c(2000) = 800
- dc/dr at r=2000 = 0.35
- Δr = 2100 - 2000 = 100
Plugging the values into the equation, we get:
c(2100) ≈ 800 + 0.35 * 100 = 835
Therefore, we estimate that c(2100) is approximately 835.