if the rate of growth of the population of deer in a forest is modeled by R(t)= 2000e^(0.23t) deer per year, where t is the number of years from today, by how many deer has the population grown in 3 years?

Q: Pilar owns a parcel of land whose value tyears from now will be V (t) = 8000e" dollars. If the…

A: Given: Pilar owns a parcel of land whose value t years from now will be V(t) = 8000et dollars. The…

Q: A right triangle has legs of 30 inches and 40 inches whose sides are changing. The short leg is…

A:

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a…

A:

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

A:

Q: You have a large metal box filled with honey, where the width is 14 cm, the length is half its size,…

A: For the metal box, it is given that width is b=14 cm, Length is half of width, l=7 cm,  Volume is…

Q: the area of a circle is decreasing at a constant rate of 181 square centimeters per second. at the…

A: Given, dAdt=181cm2sec now we know area of circle is: A=πr2 now derivate both side w.r.t t…

Q: The population of community is known to increase at a rate proportional to the number of people…

A:

Q: A quantity with an initial value of 200 grows continuously at a rate of 55% per day. What is the…

A: Let the quantity Pn grown continuously at a rate of 55% per day. Initial quantity is P0=200.

Q: (4) If the population of bacteria in a certain region triples in 50 days. In how many days will be…

A: Assuming the rate of increase is proportional to the number of inhabitants. To find- No. of days in…

Q: Suppose income from an investment starts (at time 0) at $6000 a year and increases linearly and…

A: While calculating compound interest, the addition of interest to the principal sum of a loan or a…

Q: If the population of bacteria in a certain region triples in 30 days. In how many days will be three…

A:

Q: A right triangle has legs of 3 inches and 4 inches whose sides are changing. The short leg is…

A: dhdt=7 in/sec , dbdt = -10 in/sec

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

A:

Q: A light is hung 6 meters above a straight horizontal path. If a man 2 meters tall is walking toward…

A: Decreasing:- We know that if something is decreasing then it is going down.

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

A:

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: At what rate is the production of fish changing with respect to time 5 months from now?

A: Given Data: Production of pounds of fish per month is: QK=109K13 ......1 Total investment is:…

Q: A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The length…

A: Given:A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The…

Q: The area of the expanding rectangle is increasing at the rate of 48 square centimeters per second.…

A:

Q: If

A: Explanation and solutions is given below....

Q: A quantity with an initial value of 200 grows continuously at a rate of 4% per second. What is the…

A: To find: The value of quantity after 1.55  minutes. Given: The initial value of quantity is 200 and…

Q: A rectangle has a length of 11 inches and a width of 5 inches whose sides are changing. The length…

A: In the given rectangle  Width b = 5 inches Length l = 11 inches Length increasing rate dl/dt = 9…

Q: A man 2 m tall walks toward a lamppost on level ground at a rate of 0.5 m/s. If the lamp is 5 m high…

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: A point is moving along the graph of x3y2 = 200. When the point is at (2, 5), its x-coordinate is…

A: Given that a point is moving along the graph x3y2=200 and it's x-coordinate is changing at the rate…

Q: The population of Glenbrook is 375,000and is increasing at the rate of 2.25% per year. Predict when…

A: To find: When the population is 1 million. Given: Initial population is 375000 and rate of…

Q: A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. What is the…

A:

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

A:

Q: A bacteria culture is known to grow at a rate proportional to the amount present. If the population…

A: This is a problem of the application of differential equations.

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: to find:- dH/dt.

Q: A right triangle has legs of 27 inches and 36 inches whose sides are changing. The short leg is…

A: Given that  Right triangle has  AB = 27 inches  BC = 36 inches Rate of change of short leg i.e. 27…

Q: How to solve for the second derivative?

A: The objective is to solve for the second derivative. Consider a function fx=3x4

Q: Suppose the amount of oil pumped from one of the canyon wells in Whittier, California, decreases at…

A: To determine the time (in years), the output of well fall to 1/5 of its present value.

Q: (4) If the population of bacteria in a certain region triples in 15 days. In how many days will be…

A: Bacteria increases proportional during the period given in the problem

Q: If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A:

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

A:

Q: A rectangle has a length of 11 inches and a width of 10 inches whose sides are changing. The length…

A:

Q: A bacteria grows proportional to the square root of its current population. Starting at an initial…

A:

Q: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

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: proportional

A: We will solve the problem.

Q: A light is hung 7m above straight horizontal path. If a man 2meters tall is walking toward a light…

A:

Q: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

A:

Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.