Section 8.1 « Difference Equations to Differential Equations

Section 8.1

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1. (a) $\displaystyle{x(t) = \frac{1}{3}t^3 - 2t + 3}$

(c) $\displaystyle{y(t) = \frac{2}{3}t^{\frac{3}{2}} - \frac{11}{3}}$

3. (a) $\displaystyle{x(t) = -16t^2 + 20t + 100}$

(b) $\displaystyle{t = \frac{5}{8}}$ seconds

(c) $106.25$ feet

(d) $\displaystyle{t = \frac{5}{8}(1 + \sqrt{17}) = 3.2019}$ seconds, rounded to 4 decimal places

4. (a)

(c)

(e)

(g)

5. (a)

(c)

(e)

(g)

7. (b)

(c) Yes, the object appears to be approaching a terminal speed of $1024$ feet per second.

(d) The solution, $\displaystyle{s = \frac{1024}{c^2}}$ , is the terminal speed of the object since this is the speed at which the acceleration is $0$ .

9. (b)

(c) $70.5$ million

(d) During the year 2022

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