Give an example of an equation that will translate f(x)=e^x to the left 4 units.

Q: State the Chain Rule version of the derivative of the natural logarithmic function in your own…

A: The derivative of the composite function is known as chain rule in calculus. Consider the natural…

Q: A student is 25 years old and the world has a population of 6.2 billion. Assuming that the…

A: Given,  Student's current age = 25 Student's future age = 68 Time (t) = 68 - 25  = 43 Annual growth…

Q: What are the  Exponential Curves?

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

Q: Explain a general mathematical modeling to growth of Human population. And what will be the Iraq…

A: Let the population of Iraq at time t is:  y(t) Therefore: dydtα y

Q: Find the effective rate of interest.; For 4% compounded continuously

A: 4% compounded continuously.

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given, the population of a certain country has grown at a rate proportionalto the number of people…

Q: Find the second derivative of 1/square root of 2t

A:

Q: how long will take for an investment to double in value if the interest rate 3% APR compounded…

A: We have A(t) = 2A(0) and r = 3% = 0.03

Q: The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4…

A: We use the formula                                P = ∫0T f(t)e-rt dt

Q: A bond is purchased for $1,000 that pays 6 percent of the purchase price annually. Is the amount…

A:

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: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: From the rule of decay that is, the rate of decay is proportional to the amount of the substance…

Q: A student is 19 years old and the world has a population of 6.6 billion. Assuming that the…

A: Given Present population (P) = 6.6 Rate (R) = 0.6% Time  (n) = 72-19= 53

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

A:

Q: What rate of interest compounded continuously will yieldan effective interest rate of 6%?

A: It is given that, the effective interest rate is 6%. re=6%=0.06

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: The accumulated amount of P8000 is P10000 after 2 years, calculate the interest rate if it is…

A: The accumulated amount of $8000 is $10000 after 2 years,   We have to calculate the interest rate…

Q: what is the growth rate of the cells after 6 hours has gone by

A:

Q: If there are 520 grams of Tadioactive material with a half-life of 12 hours, how TIuch of the…

A: The material is decaying at a constant rate, every 12 hours it is getting halved.  So, it is an…

Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: The rate of a continuous money flow starts at ​$600 and increases exponentially at 4% per year for…

A: Given, Initial amount P0 = $600 R = 4% = 0.04 T = 15 years

Q: Suppose the rate of net investment is given by I (t) = Lnt, find the total capital accumulation…

A:

Q: derive a formula for the of time that takes money to increase by one and half in a bank account that…

A: We have R= 3% compounded  yearly Let say it will take t years

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

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: see attached

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 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: When do we use the Chain rule in derivates of exponential function

A:

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

A:

Q: An initial investment of $6000 grows at 5% per year. What function represents the value of the…

A: Given that initial investment made = $6000 It is said that the investment grows 5% per year. This is…

Q: Use combining functions and rates of change to solve:

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: $2000 is invested in an account that pays interest compound continuously, how long will it take to…

A: The answer is given below:

Q: Use a linear approximation to estimate log10(10.5).

A:

Q: What is the main features that introduced by the exponential function? explain using only equations.

A: An exponential function is a function in which we have the independent variable as the exponent and…

Q: Let us say that an equation for deaths in relation to the availability of healthcare services is…

A: Given information: An exponential function is given.

Q: There were around 70,000 black rhinos in the world in 1970. After that, their population declined by…

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: Please

A:

Q: The price of a computer component is decreasing at a rate of 13​% per year. State whether this…

A: The price of a computer component is decreasing at 13% per year. Now, let the initial price of the…

Q: You invest 10,000  and pay 3% interest compound continuously . How will you have in 5 years?

A: Given that You invest 10,000 and pay 3% interest compound continuously .  Now we have to find amount…

Q: Give 5 examples of derivative of exponential function with solution

A:

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: We know that the differential equation of the decaydAdt=kAwhere A = amount and k = proportionality…

Q: Write the derivative of 7 log8(x)

A: We have to find the derivative of 7 log8(x).

Q: A professor surveyed students on their study habits, where "x" is the number of hours studying and…

A: The logarithmic regression equation is used to predict the y-values that lie inside (interpolate) or…

Q: what is the Derivative of Exponential Functions?

A:

Q: Describe the Derivative of the Natural Logarithm Function?

A: We have asked to describe  the derivative of the Natural Logarithm Function.

Q: Vx2-2 y = х+4

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: