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What is the exponential function that best models the number of gnats the scientists have
gathered after the number of hours listed in the table below?

What Is The Exponential Function That Best Models The Number Of Gnats The Scientists Have Gathered After The Number Of Hours Listed In The Table Below class=

Sagot :

Sqdancefanidn

Answer:

  (b)  f(x) = 12.5(1.6^x)

Step-by-step explanation:

An exponential model is generally of the form ...

  f(x) = a·b^x

where 'a' is the initial value (for x=0), and 'b' is the growth factor, the multiplier when x increases by 1.

Growth factor

The ratio of the f(x) values for x=0 and x=1 is 20/12 ≈ 1.67. A number close to this will be the growth factor in the exponential function. There is only one answer choice showing a growth factor near 1.6. (Eliminates choices A, C, D.)

An exponential regression model can be produced by many graphing calculators and spreadsheets. The attachment shows a model that has the values matching choice B.

View image Sqdancefan
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