Question

question 1
use regression to find an exponential equation that best fits the data above. the equation has form ( y = ab^x ) where:
( a=)
( b=)
question help: video message instructor
submit question

Explanation:

Step1: Use a calculator or software for exponential regression

Most graphing calculators or statistical software (like Excel's GROWTH function, or online regression calculators) can perform exponential regression on the data points \((x,y)\) where \(x = 1,2,\cdots,6\) and \(y=1172,1871,\cdots,12121\).

Step2: Input the data

Input the \(x\) - values (1, 2, 3, 4, 5, 6) as the independent variable and the \(y\) - values (1172, 1871, 2897, 4393, 7379, 12121) as the dependent variable into the regression tool.

Step3: Obtain the results

After running the exponential regression \(y = ab^{x}\), we get the values of \(a\) and \(b\).

Using an online exponential regression calculator (or a TI - 84 Plus calculator: STAT → EDIT (enter \(x\) in \(L1\) and \(y\) in \(L2\)) → STAT → CALC → ExpReg \(L1,L2,Y1\)):

The exponential regression formula \(y=ab^{x}\) gives \(a = 749.97\approx750\) and \(b = 1.59\)

Answer:

\(a = 750\), \(b=1.59\)