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(3h) 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.

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Answer: The meaning of each term of the  Madison’s and Tyler’s expressions is mentioned below.

Step-by-step explanation:

Since, when Madison starts with a population of 1,000 amoebas that triples in size every hour for a number of hours, h.

That is, after 1 hour total number of amoebas = 3×1000 = [tex]3^1\times 1000[/tex]

After 2 hour,  total number of amoebas = 3×3000=[tex]3^2\times 100[/tex]

After 3 hour, total number of amoebas = 3×9000= [tex]3^3\times 1000[/tex]

similarly, after h hours, total number of amoebas,

f(h) = [tex]3^h\times 1000[/tex]

where, 1000 is the initial population of amoeba 3 is the growth factor of population and f(h) is the population of amoeba after h hours.

Since, when Tyler starts with a population of 1 amoeba that  increases 30% in size every hour for a number of hours.

That is, after 1 hour total number of amoebas = [tex](1+0.3)^1[/tex]

After 2 hour,  total number of amoebas =  [tex](1+0.3)^2[/tex]

After 3 hour, total number of amoebas =  [tex](1+0.3)^3[/tex]

Similarly, after h hours, total number of amoebas,

f(h) =[tex](1+0.3)^h[/tex]

Where,  1 is the initial population of amoeba, 0.3 is the growth rate and 1.3 is the growth factor.


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