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There is a hot market at school for used graduation gowns, in fact, the price is growing exponentially! Last week!
could have gotten one for $25, but today, one week later, the price is $37.50. What would the price be if I decide
to wait to buy my graduation gown at graduation, six weeks from now? Show your work.

Respuesta :

calculista

Answer:

[tex]\$284.77[/tex]

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

[tex]y=a(1+r)^x[/tex]

where

y is the price in dollars

x is the number of weeks

a is the initial value

r is the rate of change

we have

[tex]a=\$25[/tex]

substitute

[tex]y=25(1+r)^x[/tex]

Remember that

one week later, the price is $37.50

so

we have the ordered pair (1,37.50)

substitute in the exponential function

[tex]37.50=25(1+r)^1[/tex]

solve for x

[tex]37.50=25(1+r)\\r=(37.50/25)-1\\r=0.5[/tex]

substitute

[tex]y=25(1+0.50)^x[/tex]

[tex]y=25(1.50)^x[/tex]

For x=6 weeks

substitute the value of x

[tex]y=25(1.50)^6=\$284.77[/tex]

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