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.

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CR: Chapter Review
Problem 12CC
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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.
f(t) t f(t)
448.00 3 580.17
488.32 4
632.39
532.27 5
689.30
t
0
1
2
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 1.36t
Of(t) = 336 x 0.82*
f(t) = 784 x 0.55t
Of(t) = 448 x 1.09⁰
Of(t) = 672 x 1.64*
= 1.09
: 1.09
O The t values are equally spaced and the successive ratios are the same, therefore the data are exponential.
O The t values are equally spaced and the ratios are all negative, therefore the data are exponential.
O 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.
Transcribed Image Text:Show that the following data are exponential and find a formula for an exponential model. f(t) t f(t) 448.00 3 580.17 488.32 4 632.39 532.27 5 689.30 t 0 1 2 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 1.36t Of(t) = 336 x 0.82* f(t) = 784 x 0.55t Of(t) = 448 x 1.09⁰ Of(t) = 672 x 1.64* = 1.09 : 1.09 O The t values are equally spaced and the successive ratios are the same, therefore the data are exponential. O The t values are equally spaced and the ratios are all negative, therefore the data are exponential. O 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.
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