Adam wins $30 in a "spot the ball" competition. He decides to save the money and opens a saving account with the $30. After his win, he continues to put $8 into his savings account each week. Identify a rule for the linear function that describes Adam's savings. Use the rule to find the amount Adam saved during the first 5 weeks. A. f(x) = −30x + 8; $70 B.f(x) = 30x + 8; $158 C. f(x) = −8x + 30; $158 D.f(x) = 8x + 30; $70

Respuesta :

The rule for the linear function that describes Adam's savings is

f(x) = 30 + 8x OR f(x) = 8x + 30

The amount Adam saved during the first 5 weeks is $70. The correct option is D.f(x) = 8x + 30; $70

Linear functions

From the question, we are to find a rule for the linear function that describes Adam's savings

From the given information,

Adam wins $3 and he opens a saving account with the $30

and

He continues to put $8 into his savings account each week

If the number of weeks he adds $8 into his account is x,

Then,

Adam's savings after x number of weeks will be

$30 + $8x

Thus, the rule for the linear function that describes Adam's savings is

f(x) = 30 + 8x OR f(x) = 8x + 30

Now, we are to find the amount Adam saved during the first 5 weeks

Using the rule

f(x) = 30 + 8x

For the first 5 weeks, that is, x = 5

Then,

f(5) = 30 + 8(5)

f(5) = 30 + 40

f(5) = 70

Hence, the amount Adam saved during the first 5 weeks is $70. The correct option is D.f(x) = 8x + 30; $70

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