Leo bought a bulldozer for $63,103. The value of the bulldozer depreciated at a constant rate per year. The table below shows the value of the bulldozer after the first and second years:

Year 1 2
Value(in dollars) 58054.76 53410.38

Which function best represents the value of the bulldozer after t years?
a) f(t) = 58,054.76(0.92)t
b) f(t) = 63,103(0.08)t
c) f(t) = 63,103(0.92)t
d) f(t) = 58,054.76(0.08)t

Question

Leo bought a bulldozer for $63,103. The value of the bulldozer depreciated at a constant rate per year. The table below shows the value of the bulldozer after the first and second years:


Year                             1                   2
Value(in dollars)    58054.76     53410.38

Which function best represents the value of the bulldozer after t years?
a) f(t) = 58,054.76(0.92)t
b) f(t) = 63,103(0.08)t
c) f(t) = 63,103(0.92)t
d) f(t) = 58,054.76(0.08)t

danjs · Answer

$$f(t) = A*b^t$$

They give you two points, you use them to find the constants A and b

danjs · Answer

with the initial value t=0 being 63103

danjs · Answer

at time t=0   f(t) = A*1
$$b^0 = 1$$

anonymous · Answer

so what answer would it be?

danjs · Answer

Using t=0   f(0)=A

(t,f(t)) = (0 , 63103)

f(0) = A = 63103

Soyou have the value for A

danjs · Answer

$$f(t) = 63103*b^t$$

use one of the points  (t , f(t))   in the equation, and solve for b

danjs · Answer

t= 1 , f(t) = 58054.76

58054.76 = 63103*b^1

solve for b

danjs · Answer

Use that b, in 
$$f(t) = 63103*b^t$$

that is like 99% of the work, i cant do more

anonymous · Answer

b=0.92?

danjs · Answer

right

anonymous · Answer

yaay

danjs · Answer

i hope you see the process to get A and b though, in 

f(t) = A*b^t

danjs · Answer

A = initial value when t=0

danjs · Answer

then use any of the points they gave (t,f(t))   and calculate b

anonymous · Answer

would the answer be b?

danjs · Answer

you told me what the value of b is in 
b=0.92
A=initial  value =63103

f(t) =A*b^t

anonymous · Answer

i solve for t?

danjs · Answer

no, where you see A, you put 63103
     where you see b, you put 0.92

done

anonymous · Answer

oh i got 58054.76

danjs · Answer

$$f(t) = 63103*(0.92)^t$$

what are you solving, how did you get 58054.76

anonymous · Answer

oh i multiplied 36103 * 0.92

danjs · Answer

you cant do that, 0.92 is raised to a power

danjs · Answer

remember, powers are calculated before multiplication

anonymous · Answer

well whats the power

danjs · Answer

t

danjs · Answer

for any time t you choose, the function f(t) will give you a value of the bulldozer at that time

anonymous · Answer

oh ok so its c

danjs · Answer

The question is looking for the general function f(t) for the depretiation of the bulldozer

f(t) = 63103 * 0.92^t

danjs · Answer

The general exponential function looks like the form

f(t) = A*b^t

did you understand how the data from the problem was used to figure out A = 63103 and b=0.92?