Answer:
We readily separate the variables and integrate:
∫dP/P=∫(k+bcos2
t)dt
ln P=kt+(b/2)*sin2t+ln C
Clearly C = Po, so we find that P(t) = Poexp(kt + (b/2)* sin 2t). The 271- curve with the typical numerical values P_o = 100, k = 0.03, and b = 0.06. It oscillates about the curve which represents natural growth with P_o and k = 0.03. We see that the two agree at the end of each full year.
note:
find the attached graph
' 125% ' means ' 1.25 '
'of' means 'times'
1.25 times (last year) = $10.50
Divide each side
by 1.25: Last year = ($10.50) / 1.25
= $8.40 .
<span> 3/4-4z+5/4z-1/2+1/2z </span>Final result : 1 - 9z
——————
4
Step by step solution :<span>Step 1 :</span> 1
Simplify —
2
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<span>Equation at the end of step 1 :</span> 3 5 1 1
(((—-4z)+(—•z))-—)+(—•z)
4 4 2 2
<span>Step 2 :</span> 1
Simplify —
2
<span>Equation at the end of step 2 :</span> 3 5 1 z
(((—-4z)+(—•z))-—)+—
4 4 2 2
<span>Step 3 :</span> 5
Simplify —
4
<span>Equation at the end of step 3 :</span> 3 5 1 z
(((—-4z)+(—•z))-—)+—
4 4 2 2
<span>Step 4 :</span> 3
Simplify —
4
<span>Equation at the end of step 4 :</span> 3 5z 1 z
(((— - 4z) + ——) - —) + —
4 4 2 2
<span>Step 5 :</span>Rewriting the whole as an Equivalent Fraction :
<span> 5.1 </span> Subtracting a whole from a fraction
Rewrite the whole as a fraction using <span> 4 </span> as the denominator :
<span> 4z 4z • 4
4z = —— = ——————
1 4 </span>
4 5/6 is the same as 29/6.
2 2/3 is the same as 8/3.
29*8 is 208.
6*3 is 18.
208/18 simplified is 104/9.
