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Likurg_2 [28]
4 years ago
15

Write an exponential function in the form y = ab” that goes through points (0,18)and (3,9216).​

Mathematics
1 answer:
babunello [35]4 years ago
3 0

Answer:

y = 18 \cdot \left(8^x\right)

Step-by-step explanation:

The question is asking for an exponential function in the form y = a\cdot b^x. The goal is to find the value of a and b such that both (0,\, 18) and (3,\, 9216) are on the graph of this function.

Saying that a point (m,\, n) is on this function is the same as stating that if x = m, then y = a \cdot b^m = n.

  • (0,\, 18) is on y = a\cdot b^x. Therefore, when x = 0, it must be true that y = a \cdot b^0 = 18. On the other hand, any non-zero number to the 0th power is 1. Since (apparently) b \ne 0, a \cdot b^0 = a. Conclusion: a = a \cdot b^0 = 18.
  • (3,\, 9216) is on y = a\cdot b^x. Therefore, when x = 3, it must be true that y = a \cdot b^{3} = 9216. Since it is determined that a = 18, 18\, b^3 = 9216. Hence b^3 = 9216 / 18 = 512. Take the cube-root of both sides: b = \sqrt[3]{512} = 8.

Conclusion:

  • a = 18.
  • b = 8.

Therefore, y = 18\cdot \left(8^x\right).

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