Question

Question #52535

Answer 1

`color(blue)(A~~$76126.2661" to 4 decimal places")`

`color(blue)(k~~0.03949" to 5 decimal places")`

Explanation:

Given:`" "$A(2.7)^(kt) = "land value"`

`A(2.7)^(3k)=$112486.....................Equation(1)`
`A(2.7)^(7k)=$131593....................Equation(2)`
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`color(blue)("Determine "k)`

`Equation(2) -: Equation(1)`

`(cancel(Acolor(white)(.))(2.7)^(7k))/(cancel(Acolor(white)(.))(2.7)^(3k))=(cancel($)131593)/(cancel($)112486)`

`(2.7)^(4k)=(131593)/(112486)`

`4klog(2.7)=log((131593)/(112486))`

`k=log((131593)/(112486)) -:4log(2.7)`

`color(blue)(k~~0.039488" to 6 decimal places")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine A")`

Substitute for `k` in `Equation(1)`

`A=($112486)/(2.7)^(3k)`

`color(blue)(A~~$76126.2661" to 4 decimal places")`