Question

There is a hot market at school for used graduation gowns, in fact, the price is growing exponentially! Last week!

Answer 1

Answer:

$\ 284.77$

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

$y=a(1+r)^x$

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

$a=\ 25$

substitute

$y=25(1+r)^x$

Remember that

one week later, the price is $37.50

so

we have the ordered pair (1,37.50)

substitute in the exponential function

$37.50=25(1+r)^1$

solve for x

$37.50=25(1+r)\\r=(37.50/25)-1\\r=0.5$

substitute

$y=25(1+0.50)^x$

$y=25(1.50)^x$

For x=6 weeks

substitute the value of x

$y=25(1.50)^6=\ 284.77$