Answered: The exponential function f(x) = () has…

Math

Calculus

The exponential function f(x) = () has the asymptote y = This means that as x , we have () -

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.1: Exponential Functions

Problem 5E

See similar textbooks

Related questions

Q: What is the (VA) Vertical Asymptote(s) of the function f(x) = log2 ^(x-2) If possible, please…

A: Given:

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 300-cc organ at a rate of 5…

A: Given: the concentration of the drug carried by the liquid=0.1g/cc liquid enters and leaves the…

Q: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: If the base b of the exponential function is a real number between zero and 1 (0 < b < 1 ) , then…

A: Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential…

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

Q: The amount of money invested in a certain account increases according to the following function,…

A: Given , y=yoe0.0475tyo→initial amount of investment .y→amount present at time t in yearsAfter how…

Q: Graph Y1 = log(x2) and Y2 = 2 log(x) using a graphingutility. Are they equivalent? What might…

A: the two function are , y1=log(x2) and y2=2log(x) . the graph of the two function will be as follows

Q: Find the equation of the vertical asymptote f(x) = log(x – 1)

Q: Find the exponential function of the form h(x)=ba^x + c such that y=2 is a horizontal asymptote…

A: Topic:- calculus

Q: Find the equation of the vertical asymptote f(x)=log(x+5)

Q: Find a formula for the exponential function passing through the points (-1,-) and (1,8) y% =

Q: An investment will generate income continuously at the constant rate of $1000 per year for 6 years.…

A: For continuous income stream, we have

Q: Heather wants to invest $35,000 of her retirement. She can invest at 4.8% simple interest for 20 yr,…

A: Simple interest is applied only on the principal amount every year. The interest amount accumulated…

Q: Find the deri vative OF +he exponential function: y = arcsin e*

A: Given function - y = sin-1e-xDifferentiating on both sides with respect to x - dydx =…

Q: Find an exponential function with horizontal asymptote y=2 whose graph contains the points( 0,3)…

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: If f(x) and g(x) is any function then, If limx→∞f(x)g(x)=∞ then f(x) grows faster than g(x). If…

Q: A mathematical model for world population growth over short intervals is given by P P, e", where P,…

Q: Find the equation of the vertical asymptote f(x) = log(x + 5)

Q: A company is considering expanding their production capabilities with a new machine that costs…

Q: Find the equation of the vertical asymptote f(x) = log(x + 4)

A: Given, f(x)= log(x+4)

Q: Find the equation of the vertical asymptote f(x)= log(x+1)

A: The equation of the vertical asymptote f(x)= log(x+1)

Q: A continuous income stream has an annual rate of flow at time t given: f(t)=9000e^(0.12t)…

Q: Find a formula for f n x if fx = ln (x-1)

A: Given, f(x)=ln(x-1) differentiate with respect to x, f'(x)=1x-1 Again differentiate with respect to…

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that a) by using the…

Q: The exponential function f(x) = ()* has the asymptote y = This means %3D that as x 0, we have ( -

A: f(x)=12x

Q: Prove that In x lim xP for any number p > 0. This shows that the logarithmic function approaches…

A: Prove that limn→∞ ln xxP=0for any numbers P>0

Q: For the function f(x)=5.log (x* - 10x +x+30)-5, on the interval (-4, 4), approximate the local…

Q: Create two exponential functions that have a horizontal asymptote at y=3 and go through the point…

A: The solution is given below

Q: explain this. How long will it take Dio who has an investment of $200 at 4% interest compounded…

A: Given:

Q: A radioactive element decays according to the function y=yoe^-0.0388t, where t is time in years. If…

Q: Find the amount that results from the given investment. $10 invested at 9% compounded continuously…

Q: Suppose you invest R10000 over a period of 6 years. If money is compounded continuously, the annual…

Q: The exponential function f(x) = (÷) has the ---Select-- v asymptote y = () - This means that as x…

A: To calculate the horizontal asymptote, limx->inf f(x) = limx->inf (1/4)x= 0

Q: The exponential function f(x) = () + 3 has the asymptote y = This means %3D that as x , we have () +…

A: Given function is fx=12x+3

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=x2lnx gx=ln2x⇒gx=lnx2 limx→∞fxgx=limx→∞x2lnxlnx2limx→∞fxgx=limx→∞x2lnx

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=lnx, gx=ln2x

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: Find the exponential function f(x)=a whose graph is given as:

A: From the graph we can see that the value of function at x = -1 is f(-1) = 3 Now we will look the…

Q: 3. f(x) = log2 (x+7)-1 X Domain: Range: End Behavior: As x→→ f(x)→∞ As x→→_____ f(x)→→x x-intercept:…

A: Given:- f(x)=log3(x+7)-1 To find:- Domain,Range ,end behaviour,x and y intercept

Q: A company is considering expanding their production capabilities with a new machine that costs…

A: Cost of new machine = 53,000 Investment = 53000 Rate of interest, r= 0.7% per year = 0.007 Time = 9…

Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: The population of a small island is growing continuously at the rate 2% per year. Estimate to the…

Q: Find an exponential function with horizontal asymptote y = 2 whose graph contains the points (0, 3)…

A: Given: Horizontal asymptote y=2 The point (0,3) and (1,5)

Q: Find the exponential function f(x)=a whose graph is given as

A: Here we have to find the exponential function whose graph is

Q: The equation y = log(x – 5) has a vertical asymptote at: - X =

A: Consider the equation y=logx-5

Q: Suppose that a machine's production can be considered as a continuous income stream with annual rate…

Q: Find the equation of the vertical asymptote f(x)=log(x+4

A: We have to use properties of log function to solve the problem.

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: We know that from the limit method, a function fx grows faster than gx if and only if limx→∞fxgx=∞…

Q: how long will it take an investment of $25,000 to grow to $35,000 ast an anual interest rate of 5%…

Q: What happens to the graph of an exponential function when the initial value, a, is less than 0?…

Question

The exponential function f(x) = () has the
asymptote y =
This means
that as x , we have () -

Expert Solution

Step 1

Consider the provided function,

$f (x) = {(\frac{1}{2})}^{x}$

Find the asymptotes of the provided function.

Now, sketch the graph of the function,

Step by step

Solved in 2 steps with 1 images

Similar questions

The natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.
Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?
The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
The natural logarithmic function f(x)= In (x1) has the ____________ asymptote x =____.
Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?
An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?
Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.