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Sagot :
if we made the regrecion in a calculator or in Excel we can see that the equation will be:
[tex]y=33558e^{-0.22x}[/tex]and the formila of an exponent is:
[tex]y=ae^{bx}^{}[/tex]b is equal to -0.22
also b is negative so is decay function
the correlation is 33558
To find the value in 18 years we replace x equal to 18 so
[tex]\begin{gathered} y=33558e^{-0.22(18)} \\ y=33558e^{-3.96} \\ y=33558(0.02) \\ y=679.28 \end{gathered}[/tex]So in 18 years the value will be 679.28
Now for the final one we replace y for 8100 so:
[tex]8100=33558e^{-0.22x}[/tex]and we solve for x so:
[tex]\begin{gathered} \frac{8100}{33558}=e^{-0.22x} \\ \ln (0.24)=-0.22x \\ \frac{-1.43}{-0.22}=x \\ x=6.4 \end{gathered}[/tex]So in 6.4 years the cost will be 8100
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