Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept of 1.

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: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: sketch the shifted exponential curves

A: We have to sketch the shifted exponential curves: y=-ex and y=-e-x. We know the graph of ex and e-x,…

Q: Find the effective rate of interest. For 6% compounded continuously

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

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Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

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: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 6% with…

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Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

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Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: A quantity with an initial value of 480 grows exponentially at a rate such that the quantity doubles…

A: Here a value is increasing exponentially. We need to find the value after specified time.

Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: Find the derivative of y =log2x

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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: find derivative y=square root of (1+ x times e^-2x)

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Q: Find the present value of $2000 to be received in 10 years, if money may be invested at 8% with…

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Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) -1 1

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

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Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: Formula to calculate continuously compounded interest: A = Pert where, A is Amount at time t,P =…

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: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

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Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

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

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Q: 1 What is the family of the equation y %3D quadratic exponential linear

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Q: Create a function in VBA of the equation of exponential curve fitting of The Annual Revenues of…

A: it graph based problem  try to substitute each value of x from 0 to 5000 and with obtain values try…

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

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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: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

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Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Topic-basic maths

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: 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: Suppose that the half-life of a substance is 250 years. If there were initially 100 g of the…

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Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

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

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Q: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

A: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

Q: A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the…

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

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

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Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: We can find the required year in the following steps.

Q: Solve for the second derivative of the function below 3. у%3 (х— 5)*

A: Given: y = x-54 To find: Second derivative of the given function.

Q: Find the interest rate r needed for an investment of $5000 to grow to $8000 in 8 years if interest…

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Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

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Q: Find 3rd derivative if ƒ'(x) = x³.

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Q: Find the present value of $1000 payable at the end of 3 years, if money may be invested at 8% with…

A: This is a question based on compound interest. we have to calculate on the basis of continuous…

Q: When we take measurements of the same general type, a power law of the form y = ax often gives an…

A: (b)   Given that X´=log(X) and Y´=log(Y)   X Y X´ Y´ 2 1.81 0.30103 0.257679…

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

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Q: what is the Derivative of Exponential Functions?

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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: