Given that an exponential function [tex]d(x)=1,200(0.84)^{x}[/tex]
We need to determine the dependent quantity for the corresponding independent quantity.
Dependent quantity when x = -2:
The dependent quantity for x = -2 can be determined by substituting x = -2 in the function [tex]d(x)=1,200(0.84)^{x}[/tex]
Thus, we have;
[tex]d(-2)=1200(0.84)^{-2}[/tex]
[tex]d(-2)=1200(0.4172)[/tex]
[tex]d(-2)=1700.64[/tex]
Rounding off to the nearest tenth, we get;
[tex]d(-2)=1700.6[/tex]
Thus, the dependent quantity for value -2 is 1700.6
Dependent quantity when x = -1:
Substituting x = -1 in the function [tex]d(x)=1,200(0.84)^{x}[/tex], we have;
[tex]d(-1)=1200(0.84)^{-1}[/tex]
[tex]d(-1)=1200(1.1905)[/tex]
[tex]d(-1)=1428.6[/tex]
Thus, the dependent quantity for value -1 is 1428.6
Dependent quantity when x = 0:
Substituting x = 0 in the function [tex]d(x)=1,200(0.84)^{x}[/tex], we have;
[tex]d(0)=1200(0.84)^0[/tex]
[tex]d(0)=1200[/tex]
Thus, the dependent quantity for value 0 is 1200.
Dependent quantity when x = 3:
Substituting x = 3 in the function [tex]d(x)=1,200(0.84)^{x}[/tex], we have;
[tex]d(3)=1200(0.84)^3[/tex]
[tex]d(3)=1200(0.5927)[/tex]
[tex]d(3)=711.24[/tex]
Rounding off to the nearest tenth, we get;
[tex]d(3)=711.2[/tex]
Thus, the dependent quantity for value 3 is 711.2
Dependent quantity when x = 7:
Substituting x = 7 in the function [tex]d(x)=1,200(0.84)^{x}[/tex], we have;
[tex]d(7)=1200(0.84)^7[/tex]
[tex]d(7)=1200(0.2951)[/tex]
[tex]d(7)=354.12[/tex]
Rounding off to the nearest tenth, we get;
[tex]d(7)=354.1[/tex]
Thus, the dependent quantity for value 7 is 354.1
Dependent quantity when x = 14:
Substituting x = 14 in the function [tex]d(x)=1,200(0.84)^{x}[/tex], we have;
[tex]d(14)=1200(0.84)^{14}[/tex]
[tex]d(14)=1200(0.0871)[/tex]
[tex]d(14)=104.52[/tex]
Rounding off to the nearest tenth, we get;
[tex]d(14)=104.5[/tex]
Thus, the dependent quantity for value 14 is 104.5
