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

Answer:

The equation is:

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

After $t=9\ months$

Step-by-step 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

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

$(2) ^ t=\frac{1,536}{3}$

$(2) ^ t=512$

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

$t=log_2(512)$

$t=9\ months$

Answer 2

Answer:

t=9 months. hope this helps