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

Question

The exponential decay graph illustrates the expected depreciation of a new boat, which is initially valued at $3,500, over a period of 10 years. 
a. Please write an exponential function that models this depreciation. 
b. Using the function developed in part a, determine the value of the boat after 9.5 years.

Anonymous · 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.

Anonymous · 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

Anonymous · 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

Anonymous · 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

Anonymous · 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.

Anonymous

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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