document.write( "Question 883723: i need help solving this please... i have tried everything i think of but i am stuck the question is: write an exponential function whose graph passes through the points (0,-3) and (4,-48). thanks so much your help is very much appreciated. \n" ); document.write( "
Algebra.Com's Answer #533716 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
An exponential equation is given by
\n" ); document.write( "(1) y = a*(e^(bx))
\n" ); document.write( "Our job is to find the values of the constants a and b, given that the curve passes through two points of (x,y).
\n" ); document.write( "All we do is to form two equations based on the two points and solve them simultaneously for a and b.
\n" ); document.write( "First put (x,y) = (0,-3) into (1) to get
\n" ); document.write( "(2) -3 = a*(e^(b*0)) or
\n" ); document.write( "(3) -3 = a*(e^(0)) or since e^0 = 1 we have
\n" ); document.write( "(4) a = -3
\n" ); document.write( "Now we have
\n" ); document.write( "(5) y = -3*(e^(bx))
\n" ); document.write( "Now put the second point (4,-48) into (5) and get
\n" ); document.write( "(6) -48 = -3*(e^(4b)) or
\n" ); document.write( "(7) (e^(4b)) = (-48)/(-3) or
\n" ); document.write( "(8) e^(4b) = 16
\n" ); document.write( "Now take the ln of both sides of (8) to get
\n" ); document.write( "(9) 4bln(e) = ln(16) or since ln(e) = 1 we have
\n" ); document.write( "(10) 4b = ln(16) or
\n" ); document.write( "(11) b = ln(16)/4 or
\n" ); document.write( "(12) b = ln(2) giving
\n" ); document.write( "(13) y = -3*(e^((ln2)x)) which simplifies to
\n" ); document.write( "(14) y = -3*(2^x) because e^ln2 = 2
\n" ); document.write( "Answer: y = -3*(2^x)
\n" ); document.write( "Check your answer. Is y = -48 when x = 4?
\n" ); document.write( "Is (-48 = -3*2^4))?
\n" ); document.write( "Is (-48 = -3*16)?
\n" ); document.write( "Is (-48 = -48)? Yes\r
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