Suppose that the value of a piece of property has been decre

Suppose that the value of a piece of property has been decrease at a continuous rate of 5 per year and is expected to decrease in that manner. Right now , the property is worth 160,000 let v { } give the value of the property year from now

Solution

the growth / decay formula, A = Pe^rt, where \"A\" is the ending amount of whatever you\'re dealing with money

\"P\" is the beginning amount of that same \"whatever\",

\"r\" is the growth or decay rate, and \"t\" is time. The above formula is related to the compound-interest formula, and represents the case of the interest being compounded \"continuously\".

so here A= V(t)

V(t) =$160000 e^0.05t

b).

half of 160000 is 80000

so 80000 =160000e^0.05t

   ^{1/2 =} e^{0.05t
ln(1/2) = 0.05t}

^{t = 13.9}

^{by the end of the 14 th the money bomes half of the original value}