The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. write an exponential

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The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. write an exponential function for the graph. b. use the function in part a to find the value of the boat after 9.5 years.

Major Spinka DVM · Accepted Answer

y=3500e^(-k⋅9.5)Step-by-step explanation:The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. Write an exponential function for the graph.b. Use the function in part a to find the value of the boat after 9.5 years.Explanation:Exponential equation is given by y=3500⋅e^(k9.5)whereby:y: valueA: constant;k: rate of changet: time valueIn this when t =03500=A⋅e^k03500=Aafter 10 years we  have, after 9.5 years, the value of the boat is:y=3500e^(-k⋅9.5)k is the rate of change and it shows that it is negative because there is a depreciation in value. Note that the rate of change is not given in this case.

Major Spinka DVM · Answer

For the answer to the question above,  V(n) = a * b^n, where V(n) shows the value of boat after n years. V(0) = 3500 V(2) = 2000  n = 0 V(0) = a * b^0 = 3500 a = 3500 V(2) = a * b^2 2000 = 3500 * b^2 b = sqrt (2000/3500) b ≈ 0.76 V(n) = 3500 * 0.76^n We can check it for n = 1 which is close to 2500 in the graph: V(1) = 3500 * (0.76)^1 V(1) = 2660 And in the graph we have V(3) ≈ 1500, V(n) = 3500 * (0.76)^3 ≈ 1536 Now n = 9.5 V(9.5) = 3500 * (0.76)^(9.5) V(9.5) ≈ 258

Major Spinka DVM · Answer

Part a: the formular for the exponential decay of a function is given bywhere f(t) is the value of the function after time t, is the initial value of the function (i.e. the value of the function at time t = 0), k is the decay constant and t is the time passed.given the graph showing the expected depreciation for a new boat, selling for $3500, over 10 years.thus, .from the graph, the value of the boat after 2 years is $2,000, thus we havetherefore, the exponential function for the graph is given bypart b: the value of the boat after 9.5 years is given bytherefore, the value of the boat after 9.5 years is $245.27

Major Spinka DVM · Answer

The general equation for exponential growth and decay is:A = Ao x (1+r)^twheret  = number of units of time.A = the amount after "t" units of time.Ao =  The initial amount Hence the final equation after substituting :A = 3500 x (1+r)^10

Major Spinka DVM · Answer

(a) (b) $245.27Explanation:(a)From the below graph it is clear that the graph it passes through the points (0,3500) and (2,2000).The general form of an exponential function is where, a is the initial value and b is growth or decay factor.Initial value is 3500, it means a=3500.f(x)=2000 at x=2.The exponential function for the graph is(b)We need to find the value of the boat after 9.5 years.Substitute x=9.5 in the above function.Therefore, the value of the boat after 9.5 years is $245.27.

Prof. Cristobal Welch

The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. write an exponential

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