252 Answered Questions for the topic Exponential Functions
A population, P(t) (in millions) in year t, increases exponentially. Suppose P(6)=18 and P(12)=26.
(1) Find a formula for the population in the form P(t)=ab^t. Enter the values you found for a and b in your formula in the blanks below. Round your values to 4 decimal places.a=b=(2) If P(t)=ae^kt,... more
Derivatives of Exp. Functions
Find the general formula for the nth derivative of f(x) = e^(2x). Using the formula, evaluate nth derivative at x = 2 or f^n(1/2). -----> I got f^n(x) = 2^(n)e^(2x) for the general formula but... more
College algebra Compound Question
My math teacher only showed us how to do this problem with a ti 85 graphing calculator. thats great and all but i don't own that kind of calculator so how do i go about this question with working... more
A new car is purchased for 18500 dollars. The value of the car depreciates at 10.75% per year. To the nearest year, how long will it be until the value of the car is 5000 dollars?
Question below: Need explanation. I know how to do the work but I don't really understand it
The equation of the function h is h(x)=1/2(x-2)^2. The table shows some of the values of function m. ——————————————— x ¦ 8 ¦ 10 ¦ 12 ¦ 14 ¦ —————————————— m(x) ¦ 2 ¦ 3 ¦ 4 ¦ 5... more
Question below: This is a practice question for a bigger test, I need an explanation so I can understand. Thanks
George is considering two different investment options. The first option offers 7.4% per year simple interest on the initial deposit. The second option offers a 6.5% interest rate but is compounded... more
Find the pattern
x y-2 .3751 1.50 61 243 96What is the pattern?________________
What do I do in the next step?
A city’s population, P (in thousands) can be modeled by the equation P x = 130(1.03)^xWhere x is the number of years after January 2000. For what value of x does the model predict that the... more
How do I solve this? without logarithm
A fully loaded Toyota Forerunner sells for $42,000. It depreciates 12% per year from the date ofpurchase. How many years will it take to be worth half its value?I think part of the equation is... more
Math Question .
Does either y=2x or y=2x+1 represent an exponential function?
Math Question .
Carmelita's grandmother offered to sponsor her money when she competed in her swim meeting. Her grandmother said that she will give her $1 if she swims 1 lap, $3 if she swims 2 laps, $5 if she... more
The temperature of hot water cools from 100 degrees celcius to room temperature of 5 celcius. After 11 minutes the temperature of the water is 30. Question I am trying to answer: Get the value of... more
A radioactive isotope has a half-life of 20 days, and decays continuously.
a. Express the amount of an initial 100-gram sample that will remain radioactive, 𝐴(𝑡), as a function of the number of days, 𝑡.b.Based on our knowledge of the half-life, we would expect that after... more
A new car is purchased for 17000 dollars. The value of the car depreciates at 12.25% per year. What will the value of the car be, to the nearest cent, after 14 years?
Start of Questions An exponential function f ( x ) = a ⋅ b x f ( x ) = a ⋅ b x passes through the points (0, 3000) and (3, 375). What are the values of a a and b b ?
3400 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 25 years, to the nearest cent?
solve for a b c and d exponential functions
suppose 𝑓(𝑥)=𝑥+4and𝑔(𝑥)=2𝑥−5 thenA.) (𝑓∘𝑔)(𝑥)=B.) (𝑓∘𝑔)^−1(𝑥)=C.) (𝑔^−1∘𝑓^−1)(𝑥)=D.) (𝑔^-1∘f^-1)(x)=
Interpreting and Using Exponential Functions
A scientist models the number of grams of a radioactive substance with the expression 15(1/2)^(d/5), where d is the number of days since the sample was measured. After how many days has half of... more
A new car is purchased for 18000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 14 years?
A town has a population of 16000 and grows at 2% every year. To the nearest tenth of year, how long will it be until the population will reach 20100
Explain or demonstrate why the product rule of exponents, b^xb^y=b^x+y, is true for positive integer values of x and y.
An exponential function, in the for f(x)=ab^x, passes through the points (2,5) and (4,180). Find b.
exponential equation identification
Find the exponential function f(x)=Ca^x whose graph goes through the points (0,2) and (3,16). a= C=
The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) in grams of cesium-137 remaining after t years is the following function
A(t)=621(1/2)t/30 Initial grams? After 100 years?
coolsculpting is a fairly new fat-freezing procedure. One treatment dissolves about 25% of the fat cells in the treated region. a) If a patient starts wih 5 lbs of fat in the treated region, how... more