Alicia, Trish + Anya -- calc geopardy

Slope Fields

100

dy/dx = y − x. At which point will the slope be zero?
A) (1, 1)
B) (2, 2)
C) (3, 3)
D) Any point where y = x

D

300

On planet Zog a strange alien plan grows at a rate modeled by dy/dx = y(2-x), where y is the high in Zog meters of the plant and x is the number of Zog days since it gew on planet Zog. the Zognian scientists are trackign the growth. A plant, Glorbnar, was measured to be 1 Zog meter tall on day 2. 

chat is this real (2,1)

500

dy/dx = x/y

two people in your team lift the third person up into the right angle of slope at (2,1)

have fun!

Separable Differential Equations

100

Which of these DEs is not separable?
A) dy/dx = x/y
B) dy/dx = (x² + y²)
C) dy/dx = y/x
D) dy/dx = x(y − 1)

B

300

solve

dy/dx = 2x/(y-1)

y^2−2y=2x^2+C

500

differential equation: dy/dx= -x/y

use your body to demonstrate how the solution to this graph will look like

you should look like a circle

Euler's Method

100

I want to estimate y(4), i know what my dy/dx is and what y(8) is, i am doing a 8 step oiler's method, what is my change in x?

-0.5

300

dy/dx = x + y, y(0) = 1. Estimate y(1) withstep of 0.5
A) 2
B) 2.25
C) 2.5
D) 3

C

500

Use Euler’s Method with step size h=0.2 to approximate y(1), given dy/dx=y+x, and y(0)=1

round to the second decimal

2.98

Exponential Models

100

If dP/dt = 0.03P, and P(0) = 1000, what is P after 10 years?
A) 1000e^0.3
B) 1000 * 1.3
C) 1300
D) e^30

A

300

population in NY is increasing porportionally every year, in 2017, the population of NY is 300, in 2020, the population grew to 700, what will be the population in 2025?

💥 2,872 PEOPLE 💥

500

A rare radioactive isotope decays at a rate proportional to the amount present. After 5 hours, only 30% of the sample remains.
How long will it take for only 10% of the original sample to remain?
Give your answer rounded to the nearest tenth.

9.6 hours

Logistic Models

100

how does a logistic model look like generally?

______/----------

300

A logistic function has carrying capacity 500 and growth rate 0.1. What is the DE?
A) dy/dt = 0.1y
B) dy/dt = 0.1y(1 − y/500)
C) dy/dt = y² − 500
D) dy/dt = −0.1y(1 + y/500)

B

500

A population of frogs in a pond follows a logistic growth model. The carrying capacity is 500 frogs. Initially, there are 50 frogs, and after 4 weeks, the population has grown to 200 frogs.

Find the population after 10 weeks.
(Round your answer to the nearest whole number.)

454