Suppose that f is an exponential function with a percentage growth rate of 2% , and with f(0)=147. Find a formula for f . a) f(t)=0.02t+147 b) f(t)=1.02(1.47)t c) f(t)=147(1.02)t d) f(t)=147(2)t e) f(t)=147(1.20)t

Question

Suppose that f is an exponential function with a percentage growth rate of 2% , and with f(0)=147. Find a formula for f . a) f(t)=0.02t+147 b) f(t)=1.02(1.47)t c) f(t)=147(1.02)t d) f(t)=147(2)t e) f(t)=147(1.20)t

Question

Answers (1)

Relevant Questions

asked 2020-11-23

Suppose that f is an exponential function with percentage growth rate of 5% and that
f(0) = 5.
Find a formula for
f(x).
f(x) =

See answers (1)

asked 2021-05-08

Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth $25,000, and its value decreases by 15% each year; 6 years.

See answers (1)

asked 2021-05-05

The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with $\displaystyle\mu={1.5}$ and $\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}$.
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$.
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X?

See answers (1)

asked 2021-05-16

Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.

See answers (1)

asked 2021-05-29

Determine whether each function represents exponential growth or exponential decay. Identify the percent rate of change.
$\displaystyle{g{{\left({t}\right)}}}={2}{\left({\frac{{{5}}}{{{4}}}}\right)}^{{t}}$

See answers (1)

asked 2020-10-23

The close connection between logarithm and exponential functions is used often by statisticians as they analyze patterns in data where the numbers range from very small to very large values. For example, the following table shows values that might occur as a bacteria population grows according to the exponential function P(t)=50(2t):
Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800
a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.
b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.
c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.
How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?

See answers (1)

asked 2021-05-18

The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance $\displaystyle{R}_{{x}}$ is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance $\displaystyle{R}_{{y}}$. The procedure for finding the unknown resistance $\displaystyle{R}_{{x}}$ is as follows. Measure resistance $\displaystyle{R}_{{1}}$ between points A and B. Then connect A and B with a heavy conducting wire and measure resistance $\displaystyle{R}_{{2}}$ between points A and C.Derive a formula for $\displaystyle{R}_{{x}}$ in terms of the observable resistances $\displaystyle{R}_{{1}}$ and $\displaystyle{R}_{{2}}$. A satisfactory ground resistance would be $\displaystyle{R}_{{x}}{<}{2.0}$ Ohms. Is the grounding of the station adequate if measurments give $\displaystyle{R}_{{1}}={13}{O}{h}{m}{s}$ and R_2=6.0 Ohms?

See answers (1)

asked 2021-02-24

Consider the following case of exponential growth. Complete parts a through c below.
The population of a town with an initial population of 75,000 grows at a rate of 5.5% per year.
a. Create an exponential function of the form
$Q=Q0 xx (1+r)t$, (where r>0 for growth and r<0 for decay) to model the situation described

See answers (1)

asked 2021-05-09

The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$
where A is the cross-sectional area of the vehicle and $\displaystyle{C}_{{d}}$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $\displaystyle\vec{{{v}}}$. Find the power dissipated by form drag.
Express your answer in terms of $\displaystyle{C}_{{d}},{A},$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $\displaystyle{P}_{{0}}$. Suppose that the maximum speed of thee car, $\displaystyle{v}_{{0}}$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $\displaystyle{P}_{{1}}$ is 10 percent greater than the original power ($\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.

See answers (1)

asked 2021-01-17

In 1995 the population of a certain city was 34,000. Since then, the population has been growing at the rate of 4% per year.
a) Is this an example of linear or exponential growth?
b) Find a function f that computes the population x years after 1995?
c) Find the population in 2002

See answers (1)

Answer 1

We have to find formula for f if growth rate is 2% and f(0)=147
Definition of exponential function:
An exponential growth or decay function is the function which grows or shri
at some condition of growth percentage,
so equation of exponential function can be expressed as:
$f(x)=a(1+r)^x or f(x)=ab^x$ (took b=1+r)
Here,
a is the initial value
r is the growth or decay rate written in decimal
b is the factor of growth or decay
According to question,
r=2%
=$2/100$)
=0.02
so,
b=1+r
=1+0.02
=1.02
Step 2
Taking variable as t,
$f(t)=ab^t$
Therefore,
$f(t)=abt=a(1.02)^t$
Given, f(0)=147
putting t=0, we get
$f(t)=a(1.02)^t$
$f(0)=a(1.02)^0$
147=a*1
a=147
$(since, (any finite number)^0=1)$
After putting value of a we can write the formula for f,
$f(t)=147(1.02)^t$
Hence, option c) is correct.

Didn’t find what you are looking for?

Suppose that f is an exponential function with a percentage growth rate of 2% , and with f(0)=147. Find a formula for f . a) f(t)=0.02t+147 b) f(t)=1.02(1.47)t c) f(t)=147(1.02)t d) f(t)=147(2)t e) f(t)=147(1.20)t

Suppose that f is an exponential function with a percentage growth rate of 2% , and with f(0)=147. Find a formula for f . a) f(t)=0.02t+147 b) f(t)=1.02(1.47)t c) f(t)=147(1.02)t d) f(t)=147(2)t e) f(t)=147(1.20)t

Answers (1)

Relevant Questions