Write a differential formula that estimates the change in diameter D of a tree if the circumference increases from C0 to C0 +dC. Recall that C=pie*D, so you can start by solving D.     Suppose that the diameter D of a certain tree is 12inches one year. During the followng year, the circumference increased by 1.5 inches. By about how much did the diameter increase that year?

Q: The population P of a bacteria culture is modeled by *picture* , where t is the time in hours. If…

A: The population P of a bacteria culture is modeled by P=4100ekt , where t is the time in hours. The…

Q: The number N of bacteria present in a culture at time t (in hours) obeys the model N(t) = 1000e0.01t…

A: Find out the time (in hours) when the bacteria reach 1700.

Q: Approximate the change in the atmospheric pressure when the altitude increases from z=9 km to z=9.05…

A: Given:

Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

A:

Q: Use differentials to approximate the desired numbers below: a. The square root of 627 b. The cube…

A: Differentiation formulae: ddxx=12xddxxn=nxn-1 Radical to exponent property: xn=x1n Formulae of…

Q: A population of bacteria is growing according to the equation P(t) = 650e0.2t. Estimate when the…

A:

Q: A population of bacteria is growing according to the equation P(t) = 2000e0.05t. Estimate when the…

A: Given query is to find the Indicated time.

Q: Use differentials to calculate the given number.  square root 81.25 Give your answer as a decimal.…

A: Assume the function be: Now, Use

Q: A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below,…

A: The total basal metabolism is given by, ∫024R(t) dt

Q: A stone is thrown vertically upward from the top of a house 112 feet high. If it was thrown at 96…

A:

Q: The formula A= 265e0039t models the population of a particular city, in thousands, t years after…

A:

Q: e) If a female salesperson told you that she has a 2-year college degree, what is your prediction on…

A: It is given that Gender takes value 1 if salesperson is 1 and 0 if salesperson is female.

Q: An arrow is shot vertically upward at a rate of 280 feet per second. Use the projectile formula h =…

A:

Q: At the beginning of an experiment, a scientist has 180 grams of radioactive goo. After 195 minutes,…

A:

Q: is dropped from a tower, 576 ft above the ground. The object's height above ground x seconds after…

A: Topic:-  algebra

Q: Use differentials to estimate the value of (1.06)3 square root (5-(1.06)3)   Final answer : 2.33

A: Given  The expression is 1.0635-1.063 .   Formula :- Linear approximation formula  Lx≈f(a)+x-af'a

Q: The half-life of cobalt-60 (used in radiation therapy) is 5.26 years (actual data). How much of a…

A: Half life formula : A = remaining amount P =initial amount = 200 g r = 0.5  t = 26.3 years t12=5.26…

Q: A certain type of bacteria grows slowly at a rate of 0.30% per day. If 46 bacteria are present…

A: We can make it easier for you

Q: Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s.With dimensions as in…

A: Solution : L2=2.62+x2 Differentiating both side w.r.t "t"  we get, 2LdLdt=2xdxdt dxdt=LxdLdt…

Q: A population of bacteria is growing according to the equation P(t) = 400eº . Estimate when the…

A: Given:

Q: If the population of a certain county was 100,000 in 1998 and 110,315 in 2008 and the formula y =…

A: Given: The population of a certain county was 100,000 in 1998 and 110,315 in 2008. The growth of the…

Q: A car moving 20m/s, increases its speed to 60m/s. The increase in speed happens over 10 seconds.…

A: We find acceleration

Q: (ii) The value V of a Porsche 718 Cayman that is t years old can be modeled byV(t) =…

A:

Q: The population of a city is growing at a rate of 7.2% per year according to the formula P(t)=12000…

A: Given,  The population growth formulaP(t) =12000e0.072t and rate of growth r = 7.2%we have to find…

Q: The growth rate of a certain bacteria culture can be calculated using the formula G = 100048 where G…

A:

Q: A certain type of bacteria grows slowly at a rate of 0.7% per day. If 31 bacteria are present today,…

A: The equation of the model is B(t)=31e0.007t. Here B(t) is the number of bacteria at time t in days.

Q: A vehicle purchased for $22400 depreciates at a constant rate of 6%. Determine the approximate…

A: Formula:      F=P(1+r)t Where, F= future value             P= present value             r= rate of…

Q: Q10 Two cars start moving from the same point. One travels south at 88 mi/h and the other travels…

A: Given that  Two cars start moving from the same point.  One car travels South at 88 mi/h The other…

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: given: newton's law of heating tells us that the difference between the temperature of the oven and…

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: Given expression is D=3000.98t where D is the temperature difference between the oven and the potato…

Q: THE POPULATION, P, OF A CERTAIN TOWN CAN BE MODELED BY THE EQUATION P = 2,005e, WHERE t = 0…

A: The Population P , of a certain town can be modeled by the equation P = 2005 ekt             ...(1)…

Q: we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: GivenInitiall potato temp = 75° oven temp = 375°difference = 375-75difference =300°D = 300 x 0.98tD…

Q: Q5/1 -A pool of stagnant water in which a stone was thrown, causing circular waves, and at some…

A: Given that  Area waves are increasing at a rate is 21πm^2/min  Diameter=14m

Q: A population of bacteria is growing according to the equation P(t)=550e^(0.06t). Estimate when the…

A:

Q: Dr. Marina Silva, in the Journal of Mammalogy (1998), gives the following formula for the…

A:

Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

A: Solution...

Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the…

A:

Q: An arrow is shot vertically upward at a rate of 210 feet per second. Use the projectile formula h =…

A:

Q: Use differential to approximate the value e1.01.

A:

Q: A 2quart container of juice develops a leak and loses juice at an average rate of 3.3 fluid ounces…

A:

Q: The area of a circle increases at a rate of 6 cm2/s. a. How fast is the radius changing when the…

A: Given that the area of a circle increases at a rate of 6 cm2/s .

Q: A Cessna plane takes off from an airport at sea level and its altitude (in feet) at time t (in…

A: Given: ht=2000lnt+1 Rate of climb will be rate of change of height i.e. dhdt

Q: The number N of E.Coli bacteria in the millions per mililiter after t minutes can be modeled by N…

A: Coli bacteria in the millions per mililiter after t minutes can be modeled by N(t)=0.5e0.014t. It is…

Q: It is estimated that within ? years, the local newspaper circulation will be ?(?) = 100?2 + 400? +…

A: Part(a): Given function is, ct=100t2+400t+5000......(1) Differentiate the equation (1) with respect…

Q: A type of radioactive element has a daily radioactive decay rate of 0.5%. If 14 pounds of this…

A:

Q: A population of bacteria is growing according to the equation P(t) = 1050e0.21t. Estimate when the…

A: Given : P(t) = 1050 e0.21t  P = 1775

Q: Rate of Equation formed from the Newton's Law of Cooling ?

A: I am attaching image so that you understand each and every step.

Q: A population of bacteria is growing according to the equation P(t) = 650e0.14t. Estimate when the…

A:

Q: A radioactive substance has a continuous decay rate of 0.064 per minute. How many grams of a 150…

A: Using exponential decay model ,  A = A0 e - r t  A 0  = initial amount  A = after decay amount  r =…

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.