A business estimates that the value $V(t)$ of office equipment is decreasing according to the function $V(t)=4800(0.9)^{t}$, where $t$ represents the number of years that have elapsed since the equipment was purchased, and $V(t)$ is in dollars. Complete parts a to $c$

Choose the correct graph below.
A.
B.
b) Find the equipment's value after 1 year.

The value of the equipment after 1 year is $\$ 4320$
(Round to the nearest cent as needed)
c) Find the number of years that will elapse before the value of the equipment depreciates to $\$ 2400$

In $\square$ years the value of the equipment depreciates to $\$ 2400$
(Round to the nearest hundredth as needed)
Clear all

Step 1 ：Given the function \(V(t)=4800(0.9)^{t}\), where \(t\) represents the number of years that have elapsed since the equipment was purchased, and \(V(t)\) is in dollars.

Step 2 ：To find the value of the equipment after 1 year, substitute \(t=1\) into the given function to get \(V(1)=4800(0.9)^{1} = \$ 4320\).

Step 3 ：To find the number of years it will take for the equipment to depreciate to \$2400, set \(V(t)\) equal to 2400 and solve for \(t\).

Step 4 ：Solving the equation \(2400 = 4800(0.9)^{t}\) gives \(t = 6.578813478960585\).

Step 5 ：Rounding to the nearest hundredth, we get \(t = 6.58\).

Step 6 ：Final Answer: The value of the equipment after 1 year is \(\boxed{4320}\) dollars. It will take approximately \(\boxed{6.58}\) years for the value of the equipment to depreciate to \$2400.