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SAVINGS Natalie has $250 in her savings accountinto which she deposits $10 of her allowance each week. The balance of her savings account can be modeled by the function f(w) = 250 + 10w , where w represents the number of weeks. Write a function g(w) to represent the balance of Natalie's savings account if she withdraws $40 to purchase a new pair of shoes. Describe the translation of f(w) that results in g(w) .

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MrRoyal

Answer:

[tex]g(w) = 210+ 10w[/tex]

Step-by-step explanation:

Given

[tex]f(w) = 250 + 10w[/tex]

[tex]Withdrawal = \$40[/tex]

Required

Determine g(w)

First, we'll write an expression for g(w)

From the question, we understand that she withdrew $40 from her account balance in w weeks.

This implies that:

[tex]g(w) = f(w) - 40[/tex]

Where f(w) is the account balance in w weeks and $40 is the withdrawn amount

Substitute 250 + 10w for f(w)

[tex]g(w) = 250 + 10w - 40[/tex]

Collect Like Terms

[tex]g(w) = 250 - 40+ 10w[/tex]

[tex]g(w) = 210+ 10w[/tex]

Recall that:

[tex]g(w) = f(w) - 40[/tex]

This means that function f(w) when shifter by 40 units downward, gives g(w)

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