Question

Select the correct answer.

Ms. Walker's class set up an online fund with a goal to raise $1,280 to go on a field trip. Ms. Walker starts the fund by depositing $5. Each week the
balance of the fund is twice the balance of the previous week.
Which equation can be used to find the number of weeks, x, after which the balance of the fund will reach $1,280, and how many weeks will it take to
reach the class goal?
A-1,280(1/2)x=5;x=7
B-1280(1/5)x=2;x=4
C-5(2)x=1,280;x=8
D-2(5)x=1,280;x=5

Answer 1

The equation to find the number of weeks is Balance = 5 * 2^x, and it will take 8 weeks to reach the goal of $1,280.

Step-by-step explanation:

To find the number of weeks, x, after which the balance of the fund will reach $1,280, we need to use the equation for exponential growth. Since the balance of the fund doubles each week, the equation is:
Balance = 5 * 2^x
where x is the number of weeks. We can set this equation equal to $1,280 and solve for x:

5 * 2^x = 1,280

Divide both sides of the equation by 5:

2^x = 256

Next, we can express both sides of the equation as powers of 2:

x = log2(256)

Using a calculator or logarithm table, we find that log2(256) = 8. Therefore, it will take 8 weeks for the balance of the fund to reach $1,280, which is the class goal.

Answer 2

The equation to find the number of weeks needed to reach the class goal of $1,280 is d. 2(5)x = 1,280. It will take 128 weeks to reach the goal.

Step-by-step explanation:

The equation that can be used to find the number of weeks, x, after which the balance of the fund will reach $1,280 is option D: 2(5)x = 1,280. To solve for x, divide both sides of the equation by 2(5):

x = 1,280 ÷ 2(5)

x = 1,280 ÷ 10

x = 128

Therefore, it will take 128 weeks to reach the class goal of $1,280.