The population of a certain inner-city area is estimated to be be declining according to the model P(t)=498,000e^-0.02  Where t is the number of years from the present.  What does this model predict the population will be in 13 years? Round to the nearest person.

Q: Suppose $15000 is invested at 7% interest compounded continuously. How long will it take for the…

A: Suppose $15000 is invested at 7% interest compounded continuously. How long will it take for the…

Q: The half-life of Erbium-171 is 7.5 hours. What is the hourly decay rate? Express the result to four…

A:

Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A:

Q: A student is 25 years old and the world has a population of 6.2 billion. Assuming that the…

A: Given,  Student's current age = 25 Student's future age = 68 Time (t) = 68 - 25  = 43 Annual growth…

Q: What is the total amount of 24000 TL with 4,8 % continuously compound interest after 5 years?

A: Consider the formula for continuous compounding, A=P·er·tHere,P=principalr=rate of interestt=time…

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given, the population of a certain country has grown at a rate proportionalto the number of people…

Q: What is the total amount of 4500 TL with 3,7 % continuously compound interest after 3 years?

A: Given Present value (P)= 4500 TL Rate (r)=3.7% Number of years (t)= 3

Q: how long will take for an investment to double in value if the interest rate 3% APR compounded…

A: We have A(t) = 2A(0) and r = 3% = 0.03

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: Suppose the population of a city has been growing at a rate of 2.5% per year for each of the last 8…

A:

Q: Suppose that a population grows according to a logistic model with carrying capacity 6500 and k =…

A:

Q: A student is 19 years old and the world has a population of 6.6 billion. Assuming that the…

A: Given Present population (P) = 6.6 Rate (R) = 0.6% Time  (n) = 72-19= 53

Q: What rate of interest compounded continuously will yieldan effective interest rate of 6%?

A: It is given that, the effective interest rate is 6%. re=6%=0.06

Q: The mass reaches 75 grams after t= years.

A:

Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: $400 invested at 7% compounded continuously after aperiod of 3 years

A:

Q: The rate of a continuous money flow starts at ​$600 and increases exponentially at 4% per year for…

A: Given, Initial amount P0 = $600 R = 4% = 0.04 T = 15 years

Q: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

A:

Q: If inflation grows continuously at a rate of 6% per year, how long will it take for $8 to lose half…

A:

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. What is the…

A: Given: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. To…

Q: Suppose the rate of net investment is given by I (t) = Lnt, find the total capital accumulation…

A:

Q: How long will it take for a principal of 1000 OMR to produce a future value of 2500 OMR at 10% rate…

A: If the interest is compounded continuously, then the formula used is A=Pert, where, A is the final…

Q: A material decays at the rate of 0.099% per year. How long will the material take so that only 30%…

A:

Q: Suppose you have a 1024 mg sample of a substance known to have a half-life of 50 years. Find the…

A: Given half-life of sample=50 yrs and the initial sample is = 1024mg.

Q: Carbon extracted from an ancient skull combined only one-sixth as much as C14 as carbon extracted…

A: Let's find age of skull.

Q: Interest is compounded continuously at 5%.  How long until a $5000 investment grows to $12000?

A: Interest is compounded continuously at 5% $5000 investment grows to $12000

Q: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

A:

Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Topic-basic maths

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: Here we will find the number of hours  for sample to double its size,

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: We have to find the growth rate.

Q: Find the effective rate of interest for 10% compound continuously.

A: The continuous rate is calculated by raising the number "e" (approximately equal to 2.71828) to the…

Q: A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the…

A:

Q: A biology experiment begins with 5 cells. In four days, the experiment grows to 164 cells. Assuming…

A:

Q: An environmental study of a certain community suggests that t years from now the level of carbon…

A: Let's find.

Q: A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is…

A: Initial Value=  8200. Growth rate= 0.55% . We can formulate the following equation for "t" years :…

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

A:

Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

A:

Q: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

A:

Q: A quantity with an initial value of 510 grows exponentially at a rate such that the quantity doubles…

A:

Q: An unknown radioactive element decays into non-radioactive substances. In 880 days, the…

A: The half life of a radioactive element is the time it takes to decay half of its original isotope.…

Q: A quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is…

A:

Q: Suppose a variable is growing continuously at a nominal rate of 10% per year. What is the effective…

A:

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A:

Q: A radioactive substance is known to have a half-life of 78 years. Calculate the number of years it…

A:

Q: consider an investment where $42000 is invested for 15 years at 6% compounded continuously. how much…

A: Given  Invested amount = $42000 interest rate = 6 % compounded continuously  time = 15 years

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.