Answer:
The value after 11 years would be: 2880 us dollars
Step-by-step explanation:
Given the function
[tex]v\left(t\right)=32,000\left(0.80\right)^t[/tex]
The initial value is basically the first output value when the input value = 0.
Here,
The initial value can be obtained by putting t=0 in the function
[tex]v\left(0\right)=32,\:000\left(0.80\right)^0[/tex]
[tex]\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0[/tex]
[tex]0.8^0=1[/tex]
Thus,
[tex]v\left(0\right)=32000\cdot \:\:1[/tex]
[tex]=32000[/tex]
Thus, initial value = v(0) = 32000
Value after 11 years can be obtained by putting t=11 in the function
[tex]v\left(11\right)=32,\:000\left(0.80\right)^{11}[/tex]
as
[tex]0.8^{11}=0.09[/tex]
so the expression becomes
[tex]v(11)=32000\cdot \:\:0.09[/tex]
[tex]=2880[/tex] us dollars
Thus, the value after 11 years would be: 2880 us dollars
