Michael starts a website for people in his town to share news and photos. Before launching the website, he has his friends and family sign up. Then, he uses the equation shown to estimate the number of users, y, who will have signed up x weeks after he officially launches the website. `y=82(1.045)^{x}`   Part A: What is the rate of growth Michael expects each week after launching the website? Part B: How many users should Michael expect after the first month? Show your work.

Q: Peter has decided to save money roughly P25 per week. Suppose he makes weekly deposits of this money…

A: Solution

Q: Find the half-life (in hours) of a radioactive substance that is reduced by 2020 percent in 55 hours…

A:

Q: The half-life of a substance is 1200 years. If the initial amount of the substance is 300 grams,…

A:

Q: Piper invested $900 in an account in the year 2009, and the value has been growing exponentially at…

A:

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: From the rule of decay that is, the rate of decay is proportional to the amount of the substance…

Q: 1) loga(3-1ogalx-)=2

A:

Q: How long does it take for $350 to grow to $840 at 6% annual percentage rate compounded continuously…

A: Continuously compounded interest formulaA= PertP = the initial principlee = natural baser = annual…

Q: A radium isotope decays exponentially and its half-life is 1600 years. Using the equation A(t)…

A: Given Half time = 1600 years At=A0e-kt

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A: Solution

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: The number of women graduating from​ 4-yr colleges in a particular country grew…

A: let the exponential function is   P(t) =P0 ert

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

A:

Q: The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional…

A: From the problem, we know that -The growth rate of the bacterium found in the human intestine is…

Q: Suppose an unknown radioactive substance produces 22400 counts per minute on a Geiger counter at a…

A:

Q: In 2000, the population of Israel was approximately 6.04 million and by 2050 it is projected to grow…

A: The explicit form of the exponential growth model is defined as At=A0ekt. Where, A(t) denotes the…

Q: The drug valium is eliminated from the bloodstream exponentially witha half-life of 36 hours.…

A:

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: Among various populations of plants or animals, diseases spread exponentially. Use the function…

A:

Q: An investment earns 5.1% yearly interest compounded continuously and is currently growing at the…

A: Solution:Given    i=5.1%     n=1     A=765   To find P=?Formula:A=P(1+i)n

Q: Determine how long it will take for an initial investment to double if it earns 7% interest per year…

A: The time take to double the initial investment is approximately 10 years  see the calculation below

Q: At the start of the year 2022, the world's population will be around 4.5 billion. The current growth…

A:

Q: The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have…

A:

Q: The growth rate of a colony of rabbits is 40% per month. If the initial population of the colony 100…

A: The initial population of the rabbits is 100. It is given that the growth rate of rabbits is 40% per…

Q: Three thousand dollars is deposited in the bank at 4% interest compounded continuously. What will be…

A: It is given that Money in the account $3000 Interest rate   We have to find the average value of…

Q: A house was valued at $190,000 in the year 1988. The value appreciated to $250,000 by the year 2003.…

A: House Price was 1,90,000 in year 1988. P=$1,19,000 The value appreciated to $250,000 by the year…

Q: The value of a savings bond is growing by 2.8% per year compounded continuously. At this growth…

A:

Q: A city has 1000 individuals and its population doubles every 60 years. Give an exponential model for…

A:

Q: The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours.…

A: Given that the initial dose is 40 milligrams of valium at midnight. The half-life of valium is 36…

Q: The drug Valium is eliminated from the bloodstream exponentially with the half-life of 36 hours.…

A: Given,

Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

A:

Q: An initial investment of $6000 grows at 5% per year. What function represents the value of the…

A: Given that initial investment made = $6000 It is said that the investment grows 5% per year. This is…

Q: In a laboratory experiment, the population of bacteria in a petri dish started off at 160 and is…

A:

Q: A material has an initial of 15 units. Which equation models the amount of the material y, decaying…

A:

Q: Aman with $30,000 to invest decides to diversity his investments by placing $15,000 in an account…

A:

Q: $2000 is invested in an account that pays interest compound continuously, how long will it take to…

A: The answer is given below:

Q: The average gain in life expectancy at birth in the US has remained almost constant for 150 years,…

A: Given:The average gain in life expectancy is equals to 3 months per year. Converting it in years so…

Q: An investment offers 5% interest compounded continuously. What is the amount of interest earned in 1…

A: Solved the give problem using concept of formula of Compound Interest ( C.I. )

Q: A bacteria culture starts with 100 bacteria and grows exponentially, after 1 hour the population is…

A:

Q: A population of 15,000 small deer in aspecific region has grown exponentially to 17,000 in 4 years.…

A: We know that exponential equation to express the population growth is, y=y0ekt Where y0 is initial…

Q: 6.05% interest compounded continuously?

A:

Q: The biomass of a yeast culture in an experiment is initially 29 grams. After 30 minutes the mass is…

A:

Q: You invest 10,000  and pay 3% interest compound continuously . How will you have in 5 years?

A: Given that You invest 10,000 and pay 3% interest compound continuously .  Now we have to find amount…

Q: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a…

A:

Q: Jun has decided to save money roughly P25 per week. Suppose he makes weekly deposits of this money…

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

Q: James wants to invest $8,000. He can invest the money at 7.2% simple interest for 30 yr or he can…

A:

Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

A: Let say population is P. So population at time 't' is given by P(t). Assume initial population is P0…

Q: Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon…

A: Given; A=Ao e^(-0.0001213)

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.