The rate of auto thefts triples every 6  months. Determine, to two decimal places, the base b  for an exponential model y=Ab^t of the rate of auto thefts as a function of time in months.

Q: The average profit a local store owner earns on a given day is $810 and is growing exponentially at…

A:

Q: Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18%…

A: Given: Initial population of cockroaches = 3.5 millions = 3500000  Rate of decrease = r=18%=0.18…

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

A:

Q: What are the  Exponential Curves?

A: Exponential curves is a function in which the variable appeares in theexponent and it grows…

Q: The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain…

A: Half life = 1590 years Inititial amount of sample (a0) = 300 mg Final amount of sample (af) = ?

Q: The average profit a local store owner earns on a given day is $960 and is growing exponentially at…

A:

Q: Suppose an insect population increases by a constant percentage each month. Explain why the number…

A: Exponential growth increases at an expanding rate with the rate of change for y being proportional…

Q: The derivative of an exponential function isn't always another exponential function.

A: Derivative of an exponential function is given by :ddxef(x,y,z) = ef(x, y , z). ddxf(x, y , z)

Q: The average profit a local store owner earns on a given day is \$590$590 and is growing…

A:

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

A:

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

A:

Q: On the day of a child's birth, a parent deposits $30,000 in a trust fund that pays 4% interest,…

A: it is given that, a parent deposits $30,000 in a trust fund that pays 4% interest, compounded…

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 quantity with an initial value of 980 decays exponentially at a rate of o.3% every decades. What…

A:

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. There…

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: Suppose that inflation causes the value of a dollar to decrease at a rate of 4.5%per year.  To use a…

A: Given :-  Suppose that inflation causes the value of a dollar to decrease at a rate of 4.5 % per…

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

A:

Q: The count in a bacteria culture was 800 after 10 minutes and 1200 after 35 minutes. Assuming th…

A: Please refer to the image below

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: The count in a bacteria culture was 900 after 10 minutes and 1500 after 40 minutes. Assuming the…

A: NOTE: Refresh your page if you can't see any equations. . let the exponential function is in the…

Q: The average profit a local store owner earns on a given day is \$120$120 and is growing…

A: given that average profit per day is $120 rate of growing is 76% per year we have to find profit…

Q: On the day of a child's birth, a parent deposits $30,000 in a trust fund that pays 5% interest,…

A: To find the balance in this account on the child's 24th birthday when compounded continuously

Q: Determine how much time is required for an investment to triple in value if interest is earned at…

A: Let P be the principal amount, then the triple amount of P is 3P.

Q: The U.S. Census Bureau keeps a running clock totaling the U.S. population. On September 20, 2012,…

A: Consider t be the time in years after the September 20, 2012 at 8.11 p.m. EST and y(t) be the…

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

A:

Q: A person places Php100,000 in a savings account which pays 3 percent interest per annum, compounded…

A: 2. Given that, A person places Php 100,000 in a savings account which pays 3 percent interest per…

Q: An art piece is predicted to increase in value by 50% in the first year and 25% each year from the…

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: Jose invests $10,000 at 10% interest that is compounded continuously. Which is the value after 10…

A: We have to find compound amount

Q: The number of users on a website is 490 and is growing exponentially at a rate of 65% per year.…

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: A quantity with an initial value of 2000 grows exponentially at a rate of o.35% every 2 days. What…

A: Given, A quantity with initial value of 2000 grows exponentially at a rate of 0.35 % every 2 days We…

Q: A woman invests $6400 in an account that pays 6% interest per year, compounded continuously. (a)…

A: To find the Final amount by using Compound interest, the following formula can be used…

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

A:

Q: proportional to A, weight W, and height H. A and W measurement values taken from different people…

A:

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

A: Given,

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

A:

Q: An accidental spill of 65 grams of radioactive material in a local stream has led to the presence of…

A:

Q: Suppose that a population that is growing exponentially increases from 800,000 people in 2010 to…

A: the exponential model is of the form, At=A0ekt where A0 original amount of the entity, t is the…

Q: A sample of bacteria taken from a river has an initial concentrationof 2.5million bacteria per…

A:

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

A:

Q: The rate of auto thefts doubles every 6 months. Determine, to two decimal places, the base b for an…

A: We have to find base b and  tripling time to the nearest tenth of a month.

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

A:

Q: A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

A: Given:A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

Q: Find the time it takes for $5,800 to double when invested at an annual interest rate of 5%,…

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

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.