Questions from General Calculus

Q: A colony of bacteria is growing exponentially with growth constant .4

A colony of bacteria is growing exponentially with growth constant .4, with time measured in hours. Determine the size of the colony when the colony I growing at the rate of 200,000 bacteria per hour....

Q: The population of a certain country is growing exponentially. The total

The population of a certain country is growing exponentially. The total population (in millions) in t years is given by the function P(t). Match each of the following answers with its corresponding qu...

Q: You have 80 grams of a certain radioactive material, and the

You have 80 grams of a certain radioactive material, and the amount remaining after t years is given by the function f (t) shown in Fig. 1. (a) How much will remain after 5 years? (b) When will 10 gra...

Q: A few years after money is deposited into a bank, the

A few years after money is deposited into a bank, the compound amount is $1000, and it is growing at the rate of $60 per year. What interest rate (compounded continuously) is the money earning?

Q: The current balance in a savings account is $1230, and

The current balance in a savings account is $1230, and the interest rate is 4.5%. At what rate is the compound amount currently growing?

Q: Find the percentage rate of change of the function f (t

Find the percentage rate of change of the function f (t) = 50e0.2t2 at t = 10.

Q: Differentiate the function. y = (x + 1)

Differentiate the function. y = (x + 1)3 / (x - 5)2

Q: Find E(p) for the demand function q = 4000

Find E(p) for the demand function q = 4000 - 40p2, and determine if demand is elastic or inelastic at p = 5.

Q: For a certain demand function, E(8) = 1

For a certain demand function, E(8) = 1.5. If the price is increased to $8.16, estimate the percentage decrease in the quantity demanded. Will the revenue increase or decrease?

Q: The herring gull population in North America has been doubling every 13

The herring gull population in North America has been doubling every 13 years since 1900. Give a differential equation satisfied by P(t), the population t years after 1900.