Question

If f(4)=183.07 when r=0.04 for the function f(t)=Pe* then what is the appropriate value of P?

Show work please

Answer 1

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} .
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Step-by-step 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) } ;
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→ Since we want to solve for: "P" ;
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→ (183.07) = P * e^(0.16) ;
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↔ P * e^(0.16) = (183.07) ;
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→ 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 " ;
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→ P = (183.07)/ (1.17351087099) ;
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→ 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).
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Hope this helps!
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Answer 2

Assuming
`f(t)=P e^(rt)`
when t = 4 the value of the function is 183.07.
Substitute those values and the value for r into the formula.

`183.07=Pe^(0.04*4)`

0.04 x 4 = 0.16

Divide both side by
`e^(0.16)`

`(183.07)/(e^(0.16))=P`
P is approximately 156.002