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Cindy plants a daffodil plant. If the plant has one daffodil flower to start with, and the number of daffodils triples every week, then how many daffodils will be there in the sixth week? Express your answer as a power, related multiplication, and in standard form. Write your answer in a sentence.

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MrRoyal

Answer:

There will be 729 daffodils in the sixth week

Step-by-step explanation:

Given

[tex]a = 1[/tex] --- start

[tex]r = 3[/tex] --- weekly rate

Required

Number of daffodils in 6th week

This question illustrates an exponential function which is represented as

[tex]f(x) = ab^x[/tex]

Where

f(x) = Number of daffodils at x week

x = The week

a = Initial number of daffodils

b= rate

So, we have:

[tex]a = 1[/tex]

[tex]b = r = 3[/tex]

Hence:

[tex]f(x) = 1 * 3^x[/tex]

[tex]f(x) = 3^x[/tex]

At the 6th week

[tex]x = 6[/tex]

So:

[tex]f(6) = 3^6[/tex] ---- as a power

[tex]f(6) = 3 * 3 * 3 * 3 * 3 * 3[/tex] --- related multiplication

[tex]f(6) = 729[/tex] --- standard form

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