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Guest Feb 23, 2015

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a).  Substitute 1 and 2 into the expression for R(n) to get two simultaneous equations for h and k:

n = 1:       h1/2/k = 4.8           (working on millions of dollars)

n = 2:       h1/k  = 5.76  from this we have h = 5.76k.  Put this into the first expression above to get:

 

(5.76k)1/2/k = 4.8    or 5.761/2/k1/2 = 4.8.   Multiply both sides by k1/2 and divide both sides by 4.8 to get:

k1/2 = 5.761/2/4.8.   Square both sides:  k = 5.76/4.82

 

$${\mathtt{k}} = {\frac{{\mathtt{5.76}}}{{{\mathtt{4.8}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.25}}$$

 

Hence from the n = 2: equation above we have h = 5.76*0.25 or 

 

$${\mathtt{h}} = {\mathtt{5.76}}{\mathtt{\,\times\,}}{\mathtt{0.25}} \Rightarrow {\mathtt{h}} = {\mathtt{1.44}}$$

 

Remember that the result of using these values in R(n) = hn/2/k will be in millions of dollars.

 

For the sum of R(n) to n, notice that it can be written as:

sum(n) = (a + a2 + a3 + ... + an)/k  where a = h1/2

The numerator is a geometric progression giving the result of sum(n) = a*(an-1)/[(a-1)k] 

or sum(n) = (h1/2)*(hn/2-1)/[(h1/2-1)k}

 

See if you can now have a go at part b).

.

Alan  Feb 23, 2015
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1+0 Answers

 #1
avatar+26406 
+10
Best Answer

a).  Substitute 1 and 2 into the expression for R(n) to get two simultaneous equations for h and k:

n = 1:       h1/2/k = 4.8           (working on millions of dollars)

n = 2:       h1/k  = 5.76  from this we have h = 5.76k.  Put this into the first expression above to get:

 

(5.76k)1/2/k = 4.8    or 5.761/2/k1/2 = 4.8.   Multiply both sides by k1/2 and divide both sides by 4.8 to get:

k1/2 = 5.761/2/4.8.   Square both sides:  k = 5.76/4.82

 

$${\mathtt{k}} = {\frac{{\mathtt{5.76}}}{{{\mathtt{4.8}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.25}}$$

 

Hence from the n = 2: equation above we have h = 5.76*0.25 or 

 

$${\mathtt{h}} = {\mathtt{5.76}}{\mathtt{\,\times\,}}{\mathtt{0.25}} \Rightarrow {\mathtt{h}} = {\mathtt{1.44}}$$

 

Remember that the result of using these values in R(n) = hn/2/k will be in millions of dollars.

 

For the sum of R(n) to n, notice that it can be written as:

sum(n) = (a + a2 + a3 + ... + an)/k  where a = h1/2

The numerator is a geometric progression giving the result of sum(n) = a*(an-1)/[(a-1)k] 

or sum(n) = (h1/2)*(hn/2-1)/[(h1/2-1)k}

 

See if you can now have a go at part b).

.

Alan  Feb 23, 2015

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