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Y_Kistochka [10]
2 years ago
7

Write an exponential model given the points ( 7, 12 ) and ( 8, 25 ). Round to the nearest hundredth.

Mathematics
1 answer:
inna [77]2 years ago
4 0

Answer:

The exponential model is y = 0.07\cdot e^{0.73\cdot x}.

Step-by-step explanation:

The exponential model can be modelled by the following mathematical expression:

y = A\cdot e^{B\cdot x} (1)

Where:

x - Independent variable.

y - Dependent variable.

A, B - Coefficients.

If we know that (x_{1}, y_{1}) = (7,12) and (x_{2}, y_{2}) = (8,25), then we get the following system of equations:

A\cdot e^{7\cdot B} = 12 (2)

A\cdot e^{8\cdot B} = 25 (3)

If we divide (3) by (2), we calculate the value of B:

e^{B}=\frac{25}{12}

B = \ln \frac{25}{12}

B \approx 0.734

And by (2), we determine the value of A:

A = 12\cdot e^{-7\cdot B}

A = 0.0704

The exponential model is y = 0.07\cdot e^{0.73\cdot x}.

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