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Show that the following data are exponential and find a formula for an exponential model. t f(t) t f(t) 0 448.00 3 580.17 1488.32 4 632.39 2 532.27 5 689.30 Complete the following table and explain how this table shows that the data are exponential. (Round your answers to two decimal places.) new f(t) old f(t) t increment 0 to 1 1 to 2 2 to 3 3 to 4 4 to 5 488.32 448.00 = 532.27 532.27 632.39 580.17 632.39 = 1.09 Find a formula for an exponential model. Of(t) = 224 x 1.36⁰ = 336 x 0.82* O f(t) = Of(t) = 784 x 0.55t f(t) = 448 x 1.09 O f(t) = 672 x 1.64⁰ = 1.09 = 1.09 The t values are equally spaced and the successive ratios are the same, therefore the data are exponential. The t values are equally spaced and the ratios are all negative, therefore the data are exponential. The t values are equally spaced and the ratios are all positive, therefore the data are exponential. O The t values are equally spaced and each ratio increases by the same amount each time, therefore the data are exponential. O The t values are equally spaced and each ratio decreases by the same amount each time, therefore the data are exponential.

Show that the following data are exponential and find a formula for an exponential model. t f(t) t f(t) 0 448.00 3 580.17 1488.32 4 632.39 2 532.27 5 689.30 Complete the following table and explain how this table shows that the data are exponential. (Round your answers to two decimal places.) new f(t) old f(t) t increment 0 to 1 1 to 2 2 to 3 3 to 4 4 to 5 488.32 448.00 = 532.27 532.27 632.39 580.17 632.39 = 1.09 Find a formula for an exponential model. Of(t) = 224 x 1.36⁰ = 336 x 0.82* O f(t) = Of(t) = 784 x 0.55t f(t) = 448 x 1.09 O f(t) = 672 x 1.64⁰ = 1.09 = 1.09 The t values are equally spaced and the successive ratios are the same, therefore the data are exponential. The t values are equally spaced and the ratios are all negative, therefore the data are exponential. The t values are equally spaced and the ratios are all positive, therefore the data are exponential. O The t values are equally spaced and each ratio increases by the same amount each time, therefore the data are exponential. O The t values are equally spaced and each ratio decreases by the same amount each time, therefore the data are exponential.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show that the following data are exponential and find a formula for an exponential model.

Show that the following data are exponential and find a formula for an exponential model. | \( t \) | \( f(t) \) | \( t \) | \( f(t) \) | |:--:|:--:|:--:|:--:| | 0 | 448.00 | 3 | 580.17 | | 1 | 488.32 | 4 | 632.39 | | 2 | 532.27 | 5 | 689.30 | Complete the following table and explain how this table shows that the data are exponential. (Round your answers to two decimal places.) | \( t \) increment | new \( f(t) \) / old \( f(t) \) | |:--:|:--:| | 0 to 1 | \(\frac{488.32}{448.00} = \) | | 1 to 2 | \(\frac{532.27}{488.32} = 1.09\) | | 2 to 3 | \(\frac{580.17}{532.27} = 1.09\) | | 3 to 4 | \(\frac{632.39}{580.17} = 1.09\) | | 4 to 5 | \(\frac{689.30}{632.39} = 1.09\) | Options: - The \( t \) values are equally spaced and the successive ratios are the same, therefore the data are exponential. - The \( t \) values are equally spaced and the ratios are all negative, therefore the data are exponential. - The \( t \) values are equally spaced and the ratios are all positive, therefore the data are exponential. - The \( t \) values are equally spaced and each ratio increases by the same amount each time, therefore the data are exponential. - The \( t \) values are equally spaced and each ratio decreases by the same amount each time, therefore the data are exponential. Find a formula for an exponential model. - \( f(t) = 224 \times 1.36^t \) - \( f(t) = 336 \times 0.82^t \) - \( f(t) = 784 \times 0.55^t \) - \( f(t) = 448 \times 1.09^
Transcribed Image Text:Show that the following data are exponential and find a formula for an exponential model. | \( t \) | \( f(t) \) | \( t \) | \( f(t) \) | |:--:|:--:|:--:|:--:| | 0 | 448.00 | 3 | 580.17 | | 1 | 488.32 | 4 | 632.39 | | 2 | 532.27 | 5 | 689.30 | Complete the following table and explain how this table shows that the data are exponential. (Round your answers to two decimal places.) | \( t \) increment | new \( f(t) \) / old \( f(t) \) | |:--:|:--:| | 0 to 1 | \(\frac{488.32}{448.00} = \) | | 1 to 2 | \(\frac{532.27}{488.32} = 1.09\) | | 2 to 3 | \(\frac{580.17}{532.27} = 1.09\) | | 3 to 4 | \(\frac{632.39}{580.17} = 1.09\) | | 4 to 5 | \(\frac{689.30}{632.39} = 1.09\) | Options: - The \( t \) values are equally spaced and the successive ratios are the same, therefore the data are exponential. - The \( t \) values are equally spaced and the ratios are all negative, therefore the data are exponential. - The \( t \) values are equally spaced and the ratios are all positive, therefore the data are exponential. - The \( t \) values are equally spaced and each ratio increases by the same amount each time, therefore the data are exponential. - The \( t \) values are equally spaced and each ratio decreases by the same amount each time, therefore the data are exponential. Find a formula for an exponential model. - \( f(t) = 224 \times 1.36^t \) - \( f(t) = 336 \times 0.82^t \) - \( f(t) = 784 \times 0.55^t \) - \( f(t) = 448 \times 1.09^
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