A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is determined that there are 450 cells present. Assuming exponential growth, determine the number of cells present at any time t (measured in minutes) and the find the doubling time.

Q: The half-life of a certain substance is 17 years. How long will it take for a sample of this…

A: The half‐life of a certain substance is 17 years. To determine how long it will take for a sample of…

Q: Suppose that $19,282 is invested at an interest rate of 5.3% per year, compounded continuously. a)…

A:

Q: 74 rabbits are released in an isolated area free of predators. After 2 years, it is estimated that…

A: Given, After 2 years, population of rabbit increased to 296 (74*4) , which is four times of initial…

Q: Assume the revenue in the year 2000 was $ 800,000, and in the year 2002 it was $ 600,000. Assuming…

A: We will use exponential growth/decay formula to find expected revenue

Q: The population of bacteria cells in a dish grows exponentially at a rate of 5% per hour. If there…

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Q: How long, to the nearest year, will it take an investment to double if it is continuously compounded…

A:

Q: The count in a bacteria culture was 200 after 20 minutes and 1200 after 30 minutes. Assuming the…

A:

Q: The count in a bateria culture was 800 after 15 minutes and 2000 after 30 minutes. Assuming the…

A: Let I be the initial size of culture,  the exponential growth formula is given by

Q: Find the time it takes for $6,400 to double when invested at an annual interest rate of 4%,…

A: Given: sum, P=$6,400 r=4%=4100=0.04 We have to find time in which given sum becomes double. So,…

Q: The count in a bacteria culture was 400 after 10 minutes and 1200 after 35 minutes. Assuming the…

A:

Q: The population of the city is declining according to the exponential law. if the population went…

A: To find the population in 2022

Q: How many years are required for an investment to double in value if it is appreciating at the rate…

A:

Q: The count in a bacteria culture was 200 after 10 minutes and 1300 after 30 minutes. Assuming the…

A: According to company policy we are allowed to provide solution for only 3 sub parts of one question.…

Q: consider an investment where $43000 is invested for years at 8% compounded continuously? how much…

A:

Q: The count in a bacteria culture was 500 after 15 minutes and 1900 after 40 minutes. Assuming the…

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Q: Taylor invested $11,000 in an account paying an interest rate of 3.5% compounded continuously.…

A: We will find out the required value.

Q: A sample of bacteria initially has 1,500 cells/L. After 5 days, the sample contains 10,000 cells/L.…

A: Given that: Initial bacterial concentration = 1500 cells/LAfter 5 days, sample contains = 10000…

Q: Find a formula for the exponential function V=h(t) that gives the value of an item initially worth…

A: Find a formula for the function exponential function v=ht that gives the value of item initially…

Q: An account now contains $3,670 and has been accumulating interest at 5% annual interest, compounded…

A: We have to find the amount in the account 5 years ago.

Q: Use the exponential decay model, A = A0ekt, to solve. Round answers to one decimal place. The…

A: Let the exponential decay model be                           A=A∘ekt As given half-life of lead is…

Q: See photo attached, thank you.

A:

Q: The half-life of a certain tranquilizer in the bloodstream is 32 hours. How long will it take for…

A:

Q: The count in a bacteria culture was 200 after 15 minutes and 1600 after 30 minutes. Assuming the…

A:

Q: Lucy invested $6,000 into an account that earns 6% interest compounded continuously. Approximately…

A: Directly use the formula for compound interest.

Q: A colony of fruit flies is growing according to the exponential law P(t) = P0ekt, and the size of…

A: Given: P(t)=P0ektwhen t=9, then P(t)P0=2

Q: How many years will it take for an invested amount of money to double its value when invested at…

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

Q: The half-life of a certain tranquilizer in the bloodstream is 44 hours. How long will it take for…

A: It is given that the half-life of a certain tranquilizer in the bloodstream is 44 hours.

Q: What amount must be invested at 9% compounded continuously, so that it will be worth $35,000 after 5…

A: The total amount (A) obtained after t years by investing an initial amount of P in a firm or account…

Q: The half-life of a certain tranquilizer in the bloodstream is 24 hours. How long will it take for…

A: Given, A= A0ekt Half life= t1/2 = 24 hours Percentage of decay= 91%

Q: suppose that the half-life of a cesium in 30 years.if there were initially 1000g of the substance.(…

A: The radioactive decay is modelled using the formula: N(t)=N0e-kt, where N0 is the initial amount and…

Q: How long, to the nearest year, will It take an Investment to double if it is continuously compounded…

A: An investment P compounded continuously at a rate of interest of r % per year for t years…

Q: Find the time it takes for $8,300 to double when invested at an annual interest rate of 11%,…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The initial size of a bacteria culture that grows exponentially was 10,000. After 1 day, there are…

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

A: The formula for Valium level a time t is given by N(t)) = N0 e-λt Given initial dose N0 = 20mg t1/2…

Q: Find the time it takes for $5,300 to double when invested at an annual interest rate of 9%,…

A: Solution:

Q: Oganesseon 294 has an exponential decay rate of 38.51% per millisecond what is the half life

A: Let N(t) be the amount of Oganesseon 294 at time t. Exponential decay rate is:  r = 38.51%

Q: In an effort to control vegetation overgrowth, 101 rabbits are released in an isolated area free of…

A: Initial population= 101  So the exponential equation is of the form: y=101(bx) Where x= number of…

Q: Assume that an insect population grows according to the law of exponential growth. After the third…

A:

Q: Some populations, such as bacteria, can be expected under the right conditions to show exponential…

A:

Q: A culture of 100 bacteria grows to 150 after 2 hours. How long will it take to double in size?…

A: Condition 1: At t=0, P(0)=P0=100   Condition 2: At t=2, P(2)=150   If P(t)=2P0, then find t (in…

Q: The count in a bacteria culture was 400 after 20 minutes and 1500 after 30 minutes. Assuming the…

A: The solution is given as follows

Q: Find the time it takes for $790,000 to double when invested at an annual interest rate of 19%,…

A: Solution-

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A:

Q: Use the exponential decay model, A = A0ekt, to solve. Round answers to one decimal place. The…

A: Given  we have to use  A = A0ekt The half life of thorium is 7340 years

Q: A house purchased for $20,000 at an interest rate of 2% and was just sold for $60,000. Assuming…

A:

Q: How long will it take a $600 investment to be worth $700 if it is continuously compounded at 11% per…

A: Write the continuous compound interest formula,

Q: The count in a bacteria culture was 200 after 20 minutes and 1700 after 35 minutes. Assuming the…

A:

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: Let the amount of aspirin in bloodstream at time t be N(t) and initial the amount be N0. Therefore…

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.