Use the exponential regression equation that best fits the data ( 10 , 4 ) , ( 12 , 20 ) , ( 13 , 35 ) , and ( 16 , 300 ) to estimate y when x = 15.

Using the exponential regression calculator, the exponential model created by the data is and the estimated y value at x = 15 is 149.944

Given the data:

( 10 , 4 ) , ( 12 , 20 ) , ( 13 , 35 ) , and ( 16 , 300 )

Using technology, the exponential model obtained using the data is :

Using the model, the predicted value of y at x = 15 :

y = 149.944

Therefore, the estimated y value is 149.944

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The exponential regression equation in general has form

The attached graph shows the exponential curve that best fits given data. From the graph it is seen that

then the exponential function is

When x=15,

147

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12