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What is the equation of the exponential curve that passes through the points (0,3) and (5,96)?

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8 votes

Final answer:

To find the equation of the exponential curve that passes through the points (0,3) and (5,96), we can use the general form of an exponential equation: y = ab^x, where a is the initial value and b is the growth/decay factor. Substitute the points into the equation to get two equations. Divide the second equation by the first equation to eliminate a and solve for b. Finally, substitute the value of b back into either of the original equations to find a. Therefore, the equation of the exponential curve is y = 3(2^x).

Step-by-step explanation:

To find the equation of the exponential curve that passes through the points (0,3) and (5,96), we can use the general form of an exponential equation: y = ab^x, where a is the initial value and b is the growth/decay factor. Substitute the points into the equation to get two equations:

  1. 3 = ab^0 -> a = 3
  2. 96 = ab^5

Divide the second equation by the first equation to eliminate a and solve for b: b^5 = 96/3 = 32. Take the fifth root of both sides to get b = 2.

Finally, substitute the value of b back into either of the original equations to find a: 3 = a(2^0) = a, so a = 3.

Therefore, the equation of the exponential curve is y = 3(2^x).

User Latanya
by
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3 votes

Answer:

M=93/5

Step-by-step explanation:

User Misha Brukman
by
8.7k points

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