What is the exponential regression equation that fits these data

Mathematics

2 answers:

s2008m [1.1K]4 years ago

7 0

Answer:

Correct choice is B.

Step-by-step explanation:

Plot the data from the given table on the coordinate plane.

Note that option C and D represent the quadratic and linear regressions (not exponential), thus, these options are false.

Plot both graphs from options A and B. The exponential regression from option A is shown by red curve (see attached diagram) and the the exponential regression from option B is shown by blue curve. As you can see the green points better suit blue curve, thus, option B is correct.

<u>Remark:</u>

Note that

$\dfrac{570}{240}, \dfrac{240}{85}, \dfrac{85}{27}, \dfrac{27}{8}, \dfrac{8}{3}$ are greater than 1.03, then option A is false.

weqwewe [10]4 years ago

6 0

C and D are not exponential functions, so eliminate C and D.
Between A and B, B is the better fit.

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A large corporation starts at time t = 0 to invest part of its receipts continuously at a rate of P dollars per year in a fund f

Andrews [41]

Answer:

$A = \frac{P}{r}\left( e^{rt} -1 \right)$

Step-by-step explanation:

This is <em>a separable differential equation</em>. Rearranging terms in the equation gives

$\frac{dA}{rA+P} = dt$

Integration on both sides gives

$\int \frac{dA}{rA+P} = \int dt$

where $c$ is a constant of integration.

The steps for solving the integral on the right hand side are presented below.

$\int \frac{dA}{rA+P} = \begin{vmatrix} rA+P = m \implies rdA = dm\end{vmatrix} \\\\\phantom{\int \frac{dA}{rA+P} } = \int \frac{1}{m} \frac{1}{r} \, dm \\\\\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \int \frac{1}{m} \, dm\\\\\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \ln |m| + c \\\\&\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \ln |rA+P| +c$