Approximating Sums and Interpretation (1) The rate at which a bean plant grows is given by a differentiable function R(t), measured in centimeters per day, where Osts 30. A graph of the function Ris shown below along with a table of values of R(t) for selected values of t. At time t=0, the plant is 10 centimeters high. Rit) 0.8- 0.6 0.4 0.2 0.0 10 5 10 15 20 25 30 1 t 0 3 7 10 16 22 27 30 R(t) 0.11 0.33 0.53 0.66 0.75 0.66 0.45 0.26 (a) Estimate the rate at which R(t) is changing when t=7 days. (b) Using a left Riemann sum, estimate the height of the plant after 16 days. Is this an overestimate or an underestimate? Justify your answer. (c) Is there any time t during the interval 0sts 30 when R'(t)=0? Explain your reasoning. (d) Use a right Riemann sum to estimate the height of the plant at the end of the 30 days. (e) Explain the meaning of R(t)dt and the plant. R(t)dtin terms of the height of (f) Suppose the height of the plant is 26 centimeters when t=27 days. Use a tangent line to approximate the height of the plant att=30 days.