Use your calculator on problems 16 - 17. Give decimal answers correct to three decimal places. 16. $f'(x) = e^{-x^2}$ and $f(3) = -1$. Find $f(2)$. 17. A cup of coffee at 93° C is put into a 20° C room when $t = 0$. The coffee's temperature is dropping at a rate of $r(t) = 5e^{-0.3t}$ °C per minute, with $t$ in minutes. Find the coffee's temperature when $t = 8$ minutes.
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To find f(2), we need to integrate f'(x) = e^(-x) to find f(x). ∫e^(-x) dx = -e^(-x) + C Since f(3) = -1, we can substitute x = 3 and f(x) = -1 into the equation above to solve for C. -1 = -e^(-3) + C C = -1 + e^(-3) Now we can find f(2) by substituting x = 2 Show more…
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