The number of bacteria in a culture is given by the function ?(?) = 350?^0.8?, where t is measured in hours. What is the initial population of the culture?

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A:

Q: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

A: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

Q: How is the natural logarithm function defined as an integral? What are its domain, range, and…

A: Explanation:

Q: A cell culture contains 7 thousand cells, and is 0.12t thousand cells growing at a rate of r(t) per…

A:

Q: A submarine started at the surface of the ocean and began diving -15 kilometers per minute towards…

A: Given: Diving speed of submarine, s = 15 km/min, and time of diving, t = 48 min

Q: Find the First Derivative: y=log10(5x+3/5x-4)

A:

Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: Give 1 problem for differentiation rule of exponential

A:

Q: A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is…

A: Here we find rate of shadow lengthening.

Q: The area of a circle is increasing at a rate of 80n square feet per second. How fast is the radius…

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: 2. Find a real root of 3x – logi0 x – 8 using the Successive Approximation method. Correct to four…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: A 10-foot ladder is standing vertically against the side of a building. To show you a related rates…

A: We can solve as follows

Q: One side of a right triangle is 150 m long and its adjacent angle is π/3 radians, with π/60 radians…

A: Possible error

Q: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04…

A: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of  0.04…

Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: The altitude of a triangle is increasing at a rate of 2.62.6 centimeters/minute while the area of…

A: Given, Area of a triangle, A=8484 cm2 Altitude of a triangle, h=1010 cm The rate of increase of…

Q: There are currently 250 cells in a culture and it grows ata rate proportional to its size. After one…

A: Given data: Total cells=250 After one hour=630

Q: A bacteria decreases at a rate of 15% continuously when exposed to ultraviolent light. If a culture…

A:

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: se Newton's Method to approximate 76 correct to six decimal places.

A: Given: 764 Formula used: xn+1=xn-fxnf'xn

Q: Use logarithmic diffenentiation on an alterative method to findthe derivative of the function?

A:

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75degrees with…

A:

Q: 2. y=cot1-2x 3. y=log22x*

A:

Q: If the radius of a circle increases by 3%, use differentials to approximate the increase in the area…

A: radius of a circle increases by 3%,

Q: Determine the derivative of 6x log3(x)

A:

Q: Find the second-order derivative of the function f(x) = log5 sin x + (2x2 - 8) / (x4 - 4x2). Please…

A:

Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: The side length'of a square is decreasing at a rate of 5 kilometers per hour. At a certain instant,…

A:

Q: A 25,000 machiene depreciates linearly to 0 over a ten year period.What is the value of the machiene…

A: The Initial value of machine is 25000 and its depreciates linearly to 0 over a ten year period. We…

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: When a circular metal plate is heated in an oven, its radius increases at the rate of 0.02 cm/min.…

A:

Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

A:

Q: When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm…

A: Given:When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01…

Q: Suppose a tank contains 600 gallons of salt water. If pure water flows into the tank at the rate of…

A: Given a tank contains 600 gallons  of salt water. Pure water flows into the tank at the rate of 7…

Q: A boy is walking toward the base of a pole 20 m high at the rate of 1 m/sec. At what rate (in meters…

A:

Q: The radius of a circle is increasing at a constant rate of 0.2 meter per second. What is the rate of…

A: Given Where r is radius. and

Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: A 6ft tall man is walking away from a 15ft tall street lamp at the rate of 5 ft/sec. How fast is his…

A: topic - triangles and rate

Q: . A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is…

A:

Q: The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty a…

A: Where k is constant of variation.

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: Given,  The one side of a right triangle is 20 cm long and the opposite angle is measured as 30°,…

Q: A6 foot tall man is walking at a rate of 40 metres per mimite directly away from a wall with a toong…

A: Given query is to find the rate of change of height of the shadow.

Q: what is the Derivative of Exponential Functions?

A:

Q: A person is walking at a rate of 5 ft per hour toward the foot of a flag pole 60 feet high. At what…

A:

Q: A rectangular beam will be cut from a cylindrical log of radius 10 inches. Suppose that the strength…

A: Solve the given problem

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.