Question

Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month. The bike Jane wants is $1,536 at the local bike shop.

Which equation represents this situation, and after how many months, t, will Jane have enough money to purchase the bike

Answer 1

t=9 months. hope this helps

Answer 2

The equation is:

`3(2) ^ t=1,536`

After
`t=9\ months`

Explanation:

This situation can be represented by an exponential growth equation of the form

`y = a (b) ^ {t}`

Where a is the initial amount

b is the growth rate

t is the time in months

In this case the initial amount is $ 3. Then
`a=3`

if she initially saves $3 and plans to double the amount she saves each month then

`b=2`

The bike Jane wants is $1,536 at the local bike shop.

Then
`y=1,536`

The equation is:

`3(2) ^ t=1,536`

Now we solve the equation for t

`3(2) ^ t=1,536`

`(2) ^ t=(1,536)/(3)`

`(2) ^ t=512`

`log_2(2) ^ t=log_2(512)`

`t=log_2(512)`

`t=9\ months`