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Question

The following data were obtained from an experiment on 2 plant samples showing exponential growth: SampleInitial weightFinal weight (in grams)Time of growth(ingrams)seconds)A10732115B723144616
Can you determine which sample is growing faster?

A
A
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B
B
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C
They are growing at equal rates
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D
Cannot be determined
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Solution

The correct option is A A
Sample A Sample B

Given: Initial weight, W0 = 107 g

Final weight, W1 = 321 g

Time of growth, t = 15 s


Given: Initial weight, W0 = 723 g

Final weight, W1 = 1446 g

Time of growth, t = 16 s

To find: Relative growth rate, r To find: Relative growth rate, r
For exponential growth, W1=W0ert ...equation (i)
where W1 is the final size of a sample, W0 is the initial size of the sample, r is the relative growth rate, t is the time of growth and e is the base of natural logarithms.
321=107×er×153=er×15loge3=15rr=loge315r=1.09915r=0.073s1
For exponential growth, W1=W0ert ...equation (i)
where W1 is the final size of a sample, W0 is the initial size of the sample, r is the relative growth rate, t is the time of growth and e is the base of natural logarithms.
1446=723×er×162=er×16loge2=16rr=loge216r=0.69316r=0.043s1

Since the relative growth rate of sample A is higher than that of sample B, sample A is growing faster than sample B.

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