Differential equations

y = 5/√(x-3) solves a differential equation. What is the domain of y?

• x > 3

• x < 3

• -3 < x < 3

• x ≠ 3

y = e^{4x + 5} - 7 solves a differential equation. What is the range of y?

• y > -7

• y < -7

• y < 7

• y > 7

• -7 < y < 7

Write a differential equation for the statement:

"The rate of change of P is proportional to the product of the present amount and 4 - P."

• dP/dt = kP

• dP/dt = k(4 - P)

• dP/dt = kP(4-P)

• dP/dt = kP/(4-P)

Let dy/dx = 3(y - 4)(y - 7) and y > 0.

For what values of y is dy/dx > 0?

• y > 4

• y > 7

• 0 < y < 4

• 0 < y < 7

Find a solution for y if dy/dx = 2x√y and y = 4 when x = 3.

• 2√y = x² + C

• y = (x² + 25)²/4

• y = x⁴/4

• y = ¼(x² - 5)²

Which of the following functions solves dy/dt = ky?

• y = y₀e^kt

• y = mx + b

• y = a(x - h)² + k

• y = Asin[B(x - C)] + D

The number of bacteria increases at a rate proportional to the present amount. After 5 hours, there were 80 bacteria and after 8 hours, there were 120 bacteria. How many bacteria were present initially?

• 1

• About 16

• About 40

• About 53

Greenium has a half-life of 23 years and decays following the Law of Exponential Change. After how many years will 80% of an original amount have decayed?

• t = 7.4143 years

• t = 10.2646

• t = 53.4043 years

• t = 74.0341 years

Suppose you deposit $1000 in an account that pays 1.5% annual interest and the deposit grows at a rate proportional to the present amount ("compound interest"). How much money will you have after 7 years if the interest is compounded continuously?

• $1110.71

• $7,000

• $10,500

• $36,315,502.67

Which of the following does NOT represent the Law of Exponential Change?

• The more radioactive material present, the faster it decays.

• The greater your bank account, the faster it grows.

• For a given distance, as travel time increases, speed goes down.

• Moore's law states that the transistor density on integrated circuits doubles every 2 years.