2) The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is $1000. a) State the rate of change of the amount in the bank account as a differential equation.

Q: find the growth rate of

A: given function

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A: Years

Q: 4. A colony of 1560 bacteria is declining by 12.5% each day. (a) Write a formula B(t) for the number…

A: Given: A colony of 1560 bacteria is declining by 12.5% each day.

Q: When you turn 50 you have $600, 000 in a retirement account which receives 5% annually. You plan to…

A: Given that when you turn 50 you have $600, 000 in a retirement account which receives 5% annually.…

Q: If the growth rate of the number of bacteria at any time (t) is proportional to the number present…

A:

Q: Simplify '.

A: We will simplify the given expression in the following step.

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A: The rate of change of amount A with respect to time t can be denoted by dAdt. If x is directly…

Q: If the interest rate is r = 0.1(10%). the bank charge is b = 100 and the investor projects that the…

A: In the given question we have to find the initial value of amount whose final amount after three…

Q: Scientists are calculating how the mass of a potato changes in a particular solution, due to water…

A:

Q: A population of 200 rodents is growing at a rate of 5% per month. What equation model can represent…

A: The exponential growth or decay is modelled using the equation, f(t)=a(1±r)t, where a is the initial…

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A: Since you have posted multiple sub parts, we will provide solutions for only first three sub parts.…

Q: Initially 56 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

A:

Q: Find the rate of change of the arts of a rectangle at the moment when it’s sides are 40 meters and…

A: We have to find the rate if change if rectangle area.

Q: Initially 53 grams of radioactive substance was present. After 6 hours the mass had decreased by 6%.…

A:

Q: A rumor spreads around a city, which has a population of 108,000. The rate of change of the number…

A: Let y denotes the fraction of population who heard the rumorThen 108,000 -y people not heard the…

Q: A young entrepreneur borrowed $4,000 to start a small business. The interest rate on the loan was 8%…

A: To model the situation described, we can use the compound interest formula. The equation that should…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.