Unit 7 check

Unit 7 check: Differential Equations

10 questions from 7 lessons in Unit 7. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 7.1 · Sort it

No calculator. Tap an equation, then tap whether it is a differential equation.

A differential equation

Not a differential equation

Question 2 · from 7.2 · Sort it

No calculator. Each card is a function. Tap a card, then tap whether it is a solution of $\frac{d y}{d x} = - 2 y$ .

Solves it

Does not solve it

Question 3 · from 7.3 · Match

No calculator. Tap a differential equation, then tap the description of its slope field.

Question 4 · from 7.4 · Calculate

No calculator. Let $y = f (x)$ be the particular solution of $\frac{d y}{d x} = x^{2} - 2 y$ with $f (1) = 3$ . Use the line tangent to the graph of $f$ at $x = 1$ to approximate $f (1.2)$ .

Your answer

Question 5 · from 7.6 · Match

No calculator. Each differential equation is separable. Tap an equation, then its general solution.

Setup for question 6

The function $f$ is continuous on $0 \leq x \leq 8$ , and its graph is made of four line segments. Let $y = g (x)$ be the solution of the differential equation $\frac{d y}{d x} = f (x)$ with the initial condition $g (2) = 3$ .

The graph of f for x from 0 to 8, four line segments joining the points (0, -4), (2, 2), (4, 2), (6, 0) and (8, -2). It crosses the x-axis going up at x = 4/3, stays at height 2 from x = 2 to x = 4, falls to the x-axis at x = 6 and ends at -2 at x = 8. — The graph of f.

Question 6 · from 7.7 · Calculate

No calculator. What is $g (6)$ ?

Your answer

Setup for question 7

A biologist stocks a pond with fish and counts them every 2 years. She models the number of fish, $P (t)$ , $t$ years after stocking, with the differential equation $\frac{d P}{d t} = k P$ , where $k$ is a constant. The model fits her counts exactly.

Number of fish in the pond
$t$ (years)	$P (t)$ (fish)
0	400
2	600
4	900

Question 7 · from 7.8 · Calculate

No calculator. According to the model, how many fish will be in the pond at $t = 6$ ?

Your answer

Question 8 · from 7.1 · Match

No calculator. In each statement $y$ is a function of $t$ and $k$ is a constant. Tap a statement, then the equation it describes.

Question 9 · from 7.2 · Multiple choice

No calculator. Which of these functions is a solution of $\frac{d y}{d x} = 12 - 3 y$ ?

Question 10 · from 7.3 · Calculate

No calculator. The coffee's temperature satisfies $\frac{d T}{d t} = - 0.1 (T - 70)$ , with $t$ in minutes and $T$ in degrees Fahrenheit. Its slope field has $t$ on the horizontal axis and $T$ on the vertical axis. What is the slope of every segment in the row $T = 150$ ?

Your answer

0 of 10 answered.