Go back to


Newly added calculators




.....The site is being constantly updated, so come back to check new updates.....

If you find any bug or need any improvements in solution report it here

Crypto fear and greed index

Curve Fitting Of Exponential Curve online calculator


This calculator is for fitting exponential curve of the type y=ae^bx. Very detailed step by step calculation is provided.

INSTRUCTION: Use ',' or new line to separate between values

You can see a sample solution below. Enter your data to get the solution for your question

$$Equation\;of\;created\;curve\;is\; Y = 16.120101e^{0.705131x}$$

$$ \displaylines{---} $$
$$ \displaylines{The\;curve\;to\;be\;fitted\;is\;Y=ae^{bx} \\ \\ Take\;log\;on\;both\;side\;to\;the\;base\;e \\ \\ \log\;_{e}\;Y\;=\;\log\;_{e}\;a\;+\;bx \\ \\ It\;is\;in\;the\;form\;y=A+Bx.\;Where\;y\;=\;\log\;_{e}\;Y,\;A\;=\;\log\;_{e}\;a,\;B\;=\;b \\ \\ Now\;we\;have\;to\;apply\;Linear\;Regression \\ \\ Before\;applying\;we\;have\;to\;find\;y\;values\;for\;corresponding\;Y\;values \\ \\ Using\;y\;=\;\log\;_{e}\;Y \\ \\ } $$
$$ No $$
$$ Y $$
$$ y $$
$$ 1 $$
$$ 520 $$
$$ 6.253829 $$
$$ 2 $$
$$ 266 $$
$$ 5.583496 $$
$$ 3 $$
$$ 567 $$
$$ 6.340359 $$
$$ 4 $$
$$ 4149 $$
$$ 8.330623 $$
$$ 5 $$
$$ 6212 $$
$$ 8.734238 $$
$$ 6 $$
$$ 9973 $$
$$ 9.207637 $$
$$ 7 $$
$$ 11894 $$
$$ 9.383789 $$
$$ 8 $$
$$ 45000 $$
$$ 10.714418 $$
$$ Total $$
$$ $$
$$ 64.548389 $$
$$ \displaylines{} $$
$$ \displaylines{Now\;we\;have\;to\;find\;mean\;of\;x\;values \\ \\ Mean = \frac{\sum_{i=1}^{n}x_{i}}{n} \\ \\ \,=\frac{4+5+6+7+8+9+10+11}{8} \\ \\ \,=\frac{60}{8} \\ \\ \Rightarrow \bar{x}= 7.5 \\ \\ Then\;we\;have\;to\;find\;mean\;of\;y\;values \\ \\ Mean = \frac{\sum_{i=1}^{n}y_{i}}{n} \\ \\ \,=\frac{6.253829+5.583496+6.340359+8.330623+8.734238+9.207637+9.383789+10.714418}{8} \\ \\ \,=\frac{64.548389}{8} \\ \\ \Rightarrow \bar{y}= 8.068549 \\ \\ } $$
$$ No $$
$$ x_{i} $$
$$ y_{i} $$
$$ (x_{i} - \bar{x}) $$
$$ (y_{i} - \bar{y}) $$
$$ (x_{i} - \bar{x})*(y_{i} - \bar{y}) $$
$$ (x_{i} - \bar{x})^2 $$
$$ 1 $$
$$ 4 $$
$$ 6.253829 $$
$$ -3.5 $$
$$ -1.81472 $$
$$ 6.35152 $$
$$ 12.25 $$
$$ 2 $$
$$ 5 $$
$$ 5.583496 $$
$$ -2.5 $$
$$ -2.485053 $$
$$ 6.212633 $$
$$ 6.25 $$
$$ 3 $$
$$ 6 $$
$$ 6.340359 $$
$$ -1.5 $$
$$ -1.72819 $$
$$ 2.592285 $$
$$ 2.25 $$
$$ 4 $$
$$ 7 $$
$$ 8.330623 $$
$$ -0.5 $$
$$ 0.262074 $$
$$ -0.131037 $$
$$ 0.25 $$
$$ 5 $$
$$ 8 $$
$$ 8.734238 $$
$$ 0.5 $$
$$ 0.665689 $$
$$ 0.332844 $$
$$ 0.25 $$
$$ 6 $$
$$ 9 $$
$$ 9.207637 $$
$$ 1.5 $$
$$ 1.139088 $$
$$ 1.708632 $$
$$ 2.25 $$
$$ 7 $$
$$ 10 $$
$$ 9.383789 $$
$$ 2.5 $$
$$ 1.31524 $$
$$ 3.2881 $$
$$ 6.25 $$
$$ 8 $$
$$ 11 $$
$$ 10.714418 $$
$$ 3.5 $$
$$ 2.645869 $$
$$ 9.260541 $$
$$ 12.25 $$
$$ Total $$
$$ $$
$$ $$
$$ $$
$$ $$
$$ 29.615518 $$
$$ 42.0 $$
$$ \displaylines{} $$
$$ \displaylines{B= \frac{\sum_{i=1}^{n}(x_{i} - \bar{x})(y_{i} - \bar{y})}{\sum_{i=1}^{n}(x_{i} - \bar{x})^{2}} \\ \\ From\;the\;table\;total\;we\;will\;get\;numerator\;and\;denominator \\ \\ \Rightarrow \frac{29.615518}{42.0} \\ \\ \Rightarrow \mathbf{\color{Red}{0.705131}} \\ \\ A = \bar{y}-B* \bar{x} \\ \\ \Rightarrow A = 8.068549-0.705131* 7.5 \\ \\ \Rightarrow \mathbf{\color{Red}{2.780067}} \\ \\ Equation\;of\;line\;\Rightarrow\;y\;=\;A+B*x \\ \\ \Rightarrow y = 2.780067+0.705131*x \\ \\ But\;A\;=\;\log\;_{e}\;a \\ \\ \Rightarrow a\;=\;e^{A} \\ \\ \Rightarrow a\;=\;e^{2.780067} \\ \\ \Rightarrow a\;=\;16.120101 \\ \\ b\;=\;B\;=\;0.705131 \\ \\ After\;putting\;back\;these\;in\;original\;equation\;Y=ae^{bx} \\ \\ We\;get\;Y\;=\;16.120101e^{0.705131x} } $$