Question

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Suppose that a certain strain of pea plant requires 14 days to reach a height of 6 inches and 30 days to reach a height of 16 inches. What should the height of the plant be in 20 days
i have 7 days to finish my online class PLEASE HELP SPMEONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (:

Answer 1

looks like an exponential growth problem
\[H _{t}=H _{0} e ^{kt}\]
use initial values h=6 at t=0 to solve for k
it takes 16 days to go from 6 to 16 inches
\[16 = 6e ^{16k}\]
\[k = \frac{\ln(8/3)}{16}\]
now solve for h at t=6
\[H _{6} = 6e ^{\frac{6\ln(8/3)}{16}}=8.67\]