The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. How do you write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years?

1 Answer
Mar 30, 2017

#y=3500*e^(k*9.5)#

Explanation:

Exponential equations can be written simply like this:
#y=A*e^(kt)#

whereby:
#y#: value
#A#: constant;
#k#: rate of change
#t#: time since the start

In this case,
#3500=A*e^(k*0)#
#3500=A#

Hence, after 9.5 years, the value of the boat is:
#y=3500*e^(k*9.5)#

#k#, the yearly depreciation rate in this case, still being unknown and have to be derived or determined by you. Also, since it is depreciation rate, #k# is a negative value.