+0  
 
0
383
1
avatar

Guest Feb 23, 2015

Best Answer 

 #1
avatar+27062 
+10

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
 #1
avatar+27062 
+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

35 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.