Respuesta :
Assuming [tex]f(t)=P e^{rt} [/tex]
when t = 4 the value of the function is 183.07.
Substitute those values and the value for r into the formula.
[tex]183.07=Pe^{0.04*4}[/tex]
0.04 x 4 = 0.16
Divide both side by [tex]e^{0.16}[/tex]
[tex]\frac{183.07}{e^{0.16}}=P[/tex]
P is approximately 156.002
when t = 4 the value of the function is 183.07.
Substitute those values and the value for r into the formula.
[tex]183.07=Pe^{0.04*4}[/tex]
0.04 x 4 = 0.16
Divide both side by [tex]e^{0.16}[/tex]
[tex]\frac{183.07}{e^{0.16}}=P[/tex]
P is approximately 156.002
Answer:
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If "P" is the "prinicipal amount" in dollars and cents, we would round up to the nearest hundredth, or "cent" (percentage of a dollar); and the answer would be:
" $155.00 " . Otherwise, if we are talking about population, we would round to the nearest hundredth, to maintain 5 (five) significant figures, and the answer would be: " 155.00" {in some cases, "155" would suffice} .
___________________________________________________________
Explanation:
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f(t) = P*e^(r*t) ;
f(4) = P*e^(0.04 * 4) ;
Given: " f(4) = 183.07 ";
Calculate: (r*t = 0.04 * 4 = 0.16) ;
Rewrite the equation; substituting: "183.07" for "f(4)" ; {i.e., for "f(t)" } ;
and substituting: "0.16" for "(0.04* 4)" ; {i.e. for "(r*t) } ;
_______________________________________________________
→ Since we want to solve for: "P" ;
_____________________________________________
→ (183.07) = P * e^(0.16) ;
_____________________________________________
↔ P * e^(0.16) = (183.07) ;
______________________________________________
→ Divide EACH SIDE of the equation by: { "e^(0.16)" } ; to isolate "P" on one side of the equation; and to solve for "P" ;
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→ { P * e^(0.16) } / { e^(0.16) } = { 183.07 }/ { (e^(0.16) } ;
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→ P = { 183.07 }/ { (e^(0.16) } ;
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NOTE: " e^(0.16) = 1.17351087099 " ;
______________________________________________
→ P = (183.07)/ (1.17351087099) ;
______________________________________________
→ P = 156.001963446
Now, assuming "P" is the "prinicipal amount" in dollars and cents, we would round up to the nearest hundredth, or "cent" (percentage of a dollar); and the answer would be: $ 155.00 . Otherwise, if we are talking about population, we would round to the nearest hundredth, to maintain 5 (five) significant figures, and the answer would be: " 155.00 " (in some cases, simply "155" would be sufficient).
________________________________________
Hope this helps!
________________________________________
_____________________________________________
If "P" is the "prinicipal amount" in dollars and cents, we would round up to the nearest hundredth, or "cent" (percentage of a dollar); and the answer would be:
" $155.00 " . Otherwise, if we are talking about population, we would round to the nearest hundredth, to maintain 5 (five) significant figures, and the answer would be: " 155.00" {in some cases, "155" would suffice} .
___________________________________________________________
Explanation:
________________________________________________________
f(t) = P*e^(r*t) ;
f(4) = P*e^(0.04 * 4) ;
Given: " f(4) = 183.07 ";
Calculate: (r*t = 0.04 * 4 = 0.16) ;
Rewrite the equation; substituting: "183.07" for "f(4)" ; {i.e., for "f(t)" } ;
and substituting: "0.16" for "(0.04* 4)" ; {i.e. for "(r*t) } ;
_______________________________________________________
→ Since we want to solve for: "P" ;
_____________________________________________
→ (183.07) = P * e^(0.16) ;
_____________________________________________
↔ P * e^(0.16) = (183.07) ;
______________________________________________
→ Divide EACH SIDE of the equation by: { "e^(0.16)" } ; to isolate "P" on one side of the equation; and to solve for "P" ;
______________________________________________
→ { P * e^(0.16) } / { e^(0.16) } = { 183.07 }/ { (e^(0.16) } ;
______________________________________________
→ P = { 183.07 }/ { (e^(0.16) } ;
______________________________________________
NOTE: " e^(0.16) = 1.17351087099 " ;
______________________________________________
→ P = (183.07)/ (1.17351087099) ;
______________________________________________
→ P = 156.001963446
Now, assuming "P" is the "prinicipal amount" in dollars and cents, we would round up to the nearest hundredth, or "cent" (percentage of a dollar); and the answer would be: $ 155.00 . Otherwise, if we are talking about population, we would round to the nearest hundredth, to maintain 5 (five) significant figures, and the answer would be: " 155.00 " (in some cases, simply "155" would be sufficient).
________________________________________
Hope this helps!
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