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Sydney placed 10 guppies in a fish tank. She recorded the number of guppies in the tank over a period of 4 weeks in the table.
Number of Weeks
01
2
3
4
Number of Guppies 10 30 90 270 810
Create an explicit formula for the number of guppies in the tank in terms of the number of weeks, n.
Drag numbers, expressions, and symbols to the line to show the formula,

Sydney placed 10 guppies in a fish tank She recorded the number of guppies in the tank over a period of 4 weeks in the table Number of Weeks 01 2 3 4 Number of class=

Respuesta :

Answer:

g(n)= 3^n x 10

Step-by-step explanation: The numbers are increasing exponentially and are being multiplied by 30.  Since it's not a linear rate of change, it is going to be exponential, so 3 to the n power or whatever week number times 10 will give you the amount of guppies after a specific amount of weeks!

MrRoyal

The explicit equation for the number of guppies is: [tex]\mathbf{y = 10 \times 3^x}[/tex]

The table is an illustration of an exponential model.

An exponential model is represented as:

[tex]\mathbf{y = ab^x}[/tex]

Let x represents the number of weeks, and y represents the number of guppies.

When x = 0, y = 10

So, we have:

[tex]\mathbf{10 = ab^0}[/tex]

[tex]\mathbf{10 = a \times 1}[/tex]

[tex]\mathbf{10 = a}[/tex]

Rewrite as:

[tex]\mathbf{a = 10 }[/tex]

When x = 1, y =30

So, we have:

[tex]\mathbf{30 = ab^1}[/tex]

[tex]\mathbf{30 = ab}[/tex]

Substitute 10 for (a)

[tex]\mathbf{30 = 10b}[/tex]

Divide both sides by 10

[tex]\mathbf{3 = b}[/tex]

Rewrite as:

[tex]\mathbf{b = 3 }[/tex]

Substitute 3 for b and 10 for (a) in [tex]\mathbf{y = ab^x}[/tex]

Hence, the explicit equation is: [tex]\mathbf{y = 10 \times 3^x}[/tex]

Read more about explicit equations at:

https://brainly.com/question/12502099

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