Find the exponential function that models the data in the table below. begin{array}{|c|c|}x&-3& -2&-1&0&1&2&3& 4 y&4/27&4/9&4/3&4 &12 & 36 & 108 & 324end{array} What is the exponential regression of the data? y = square

rocedwrp 2020-11-26 Answered
Find the exponential function that models the data in the table below. x32101234y4/274/94/341236108324 What is the exponential regression of the data? y=square
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

crocolylec
Answered 2020-11-27 Author has 100 answers

Introduction Given a dataset where an exponential function y=abx where a and b are constants. are to be obtained. Taking logarithm on both sides of the above equation, logy=loga+xlogb v=A+Bx

where v=logy,A=loga,B=logb

Hence, the exponential function is reduced to a linear function between v and x and can be solved by least square method. By principle of least squares, the normal equations for estimating A and B is given by, v=nA+Bxvx=Ax+Bx2

Calculations The following is table is formed to calculate the value of A and B

yxv=logyx2vx4/2730.829392.48794/920.352240.70444/310.124910.1249400.6021001211.079211.07923621.556343.112610832.033496.100232442.51051610.0420Total46.72494423.4014

Hence, putting the values obtained from the table to the normal equations we get, 6.7249=8A+4B......(i)23.4014=4A+44B......(ii)

On solving the simultaneous equations, by method of comparison, it is obtained that, from (i)A=6.72494B8.....(iii)from(ii)A=23.401444B4.......(iv)

Comparing (iii) and (iv) 6.72494B8=23.401444B4 Hence solving the above equation, it is obtained that, B=0.4771 b=AntilogB =2.9999 Then putting the value of B in (iii), it is obtained that, A=0.6021 a=AntilogA =4.0004 Therefore, The required exponential regression of the data is y=4.0004(2.9999)x

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-07
A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.
asked 2021-09-17
The function y=3.5x+2.8 represents the cost y (in dollars) of a taxi ride of x miles.
a. Identify the independent and dependent variables.
b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.
asked 2021-05-25
Write an equivalent expression for 5(2x+y−3z) by modeling and by using the distributive property.
asked 2021-09-18

Whether the given data is linear or exponential and find the corresponding model.
Given: The table
x01234y20.80.41.62.8

asked 2021-03-07
A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a ?, and then, after assiging labels to the quantities, forming an ?.
asked 2021-09-15
The function represents the height y (in feet) of a grasshopper jumping straight up from the ground f seconds after the start of the jump. After how many seconds is the grasshopper 1 foot oft the ground?
Given: Function y=16t2+8t represents the height (in feet) of grasshopper at t seconds.
asked 2021-09-06
Combine the expression as a logarithm of a single expression.
Given:
The expression of a logarithm is log6+log5x