Use logarithmic regression to find an equation of the form y= a+b in(x) to model the data

A:-76.204

B:37.673

And the last one is "51"

Step-by-step explanation:

I just took the test on edge.

Logarithmic Regression:

To model a function is in the form of : ....[1] to a set of data.

Here, x represents the days and y represents the height.

Using the table as shown:

x          y

9          5

12         17

22        45

40        60

Now, create a scatter plot and a graph of the model as shown below

The command for logarithmic regression in excel is given as:

we can write this as:

on comparing with [1] we have;

a = -76.204 and b = 37.63

Therefore, the value of a and b are:  -76.204 and 37.63

and equation that model the data is,  

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt