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

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!

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2