Answer:
$94,090.
Step-by-step explanation:
We have been given that the value of a machine depreciates each year by 3%.
We can see that the value of machine is depreciating exponentially, so let us write an exponential function for the given situation.
Since we know that an exponential function is in form: [tex]y=a*b^x[/tex], where,
a = Initial value.
b = For decay function b equals (1-r), where r is rate in decimal form.
Let us convert our given rate in decimal form.
[tex]3\%=\frac{3}{100}=0.03[/tex]
Upon substituting a=1,00,000, x=2 and r=0.03 in exponential decay function we will get,
[tex]y=1,00,000(1-0.03)^2[/tex]
[tex]y=1,00,000(0.97)^2[/tex]
[tex]y=1,00,000*0.9409[/tex]
[tex]y=94,090[/tex]
Therefore, the value of the machine after 2 years will be $94,090.
