It is projected that t years after 2010, the population of the United States will be P(t)=310e^0.007t million people. What is the projected population in the year 2045?

Q: Find the missing values assuming continuously compounde interest Initial Investment: $1000 Annual…

A: Given that  Initial investment = 1000  To find time to double, we use final amount = 2(1000)=2000…

Q: Suppose that $8000 is invested at an interest rate of 5.2% per year, compounded continuously. What…

A: Principal= P= $8000 Interest rate = 5.2%= 0.052 Final amount = double of 8000=16000

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

A:

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: 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: Find the effective rate of interest.For 5% compounded continuously

A: Here we have to find the effective rate of interest. For 5% compounded continuously.  r = 5%…

Q: The initial population size was 53 hippogriffs. After only 5 year(s), a new count was taken…

A:

Q: The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4…

A: We use the formula                                P = ∫0T f(t)e-rt dt

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 that money is deposited daily into a savings account at an annual rate of $1300. If the…

A: P = $1300 r = 4% N = 4

Q: Consider a population of a certain country that is observed to grow exponentially. Based  from the…

A:

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: Find the present value of $1000 payable at the end of 3 years, if money may be invested at 8% with…

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

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Q: The accumulated amount of P8000 is P10000 after 2 years, calculate the interest rate if it is…

A: The accumulated amount of $8000 is $10000 after 2 years,   We have to calculate the interest rate…

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

A:

Q: $5,000 is invested in an account earning 6% interest (APR), compounded continuously. How much is in…

A: Total investment P=$5000 Rate of interest R= 6% Time t=3 years Total amount after 3 years

Q: As an active environmentalist who is interested in the impact of climate change on sea level, you…

A: Given: Mount Kinabalu is 4095m above sea level at the beginning of year 2015 . However, due to…

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: A certain specimen of charcoal contains 55% of Carbon – 14 as compared to a charcoal at present day.…

A: Given- X=X0e-kt  and the charcoal contains 55% of carbon as compared to present day and the value of…

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

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Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

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: 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 that money is deposited daily into a savings account at an annual rate of $1200. If the…

A: Compound interest problem.....

Q: How long will it take for $4000 to double in value if it is deposited in an account bearing 7%…

A: Continuous compound interest formula: A=Pert P-principle A-Amount r-rate t-number of years.

Q: find the present value of an investment worth $15,000 in 15 years with 5% interest compounded…

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

A: Topic-basic maths

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: As an active environmentalist who is interested in the impact of climate change on sea level, you…

A: Let Pn represents the elevation of n years for Mount Kinabalu.   At the beginning of the year…

Q: If $4,000 is invested at 8% compounded continuously, graph the amount in the account as a function…

A: P=$4,000 , r=8%=0.08 Now by using compound interest formula for continuously compounding, we have…

Q: see attached

A:

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: How long does it take to have a balance of $900 if $500 is invested at 0.75% annual interest…

A:

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

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: Find the accumulated amount after 5 years if $4500 is invested at 4%/year compounded continuously.

A:

Q: The half-life of carbon-14 is 5730 years. How long does it take for 2.1 grams of carbon-14 to be…

A: A(t)=A0(1/2)t/h h is the half life A0 is the initial value

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: Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 4 yr if…

A:

Q: Suppose that money is deposited daily into a savings account at an annual rate of $1100. if the…

A: Given  P: the principal, =$1100 t: the time= 4 years r: the rate, (in decimal form)=0.05

Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: Here, the exponential model is given by: P(t)=a×bt...(1) where P(t) is the number of cases after a…

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.