Explain what each part of Madison’s and Tyler’s expressions mean. Madison’s Expression: 1,000(3^h) h: 1,000: 3: 3^h: Tyler’s Expression: (1 + 0.3)^h h: 1 + 0.3:

Question

Madison starts with a population of 1,000 amoebas that triples in size every hour for a number of hours, h. She writes the expression 1,000(3^h) to find the number of amoeba after h hours.

Tyler starts with a population of 1 amoeba that increases 30% in size every hour for a number of hours, h. He writes the expression (1 + 0.3)^h to find the number of amoeba after h hours.

Use the drop-down menus to explain what each part of Madison’s and Tyler’s expressions mean.

Madison’s Expression: 1,000(3^h)

h:
1,000:
3:
3^h:

Tyler’s Expression: (1 + 0.3)^h

h:
1 + 0.3:

Quizzma Team · Answer

Sure! Let’s break down each part of Madison’s and Tyler’s expressions:

Madison’s Expression: 1,000(3^h)

– h: The number of hours that have passed since the initial population.

– 1,000: The initial population of amoebas at time zero.

– 3: The growth factor, which means the population triples every hour.

– 3^h: Represents the total growth factor after h hours, showing how many times the original population has increased by a factor of 3 for each hour.

Tyler’s Expression: (1 + 0.3)^h

– h: The number of hours that have passed since the initial population.

– 1 + 0.3: This represents the growth rate. The 1 corresponds to the original amount (100%), and 0.3 represents the 30% increase in population after each hour.

– (1 + 0.3)^h: This expression shows how the population grows over h hours, accounting for a 30% increase each hour.

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Explain what each part of Madison’s and Tyler’s expressions mean. Madison’s Expression: 1,000(3^h) h: 1,000: 3: 3^h: Tyler’s Expression: (1 + 0.3)^h h: 1 + 0.3:

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