Question

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?

Answer 1

Answer: $y=5(2)^x$  

It will take 8 weeks to reach the class goal.

Step-by-step explanation:

We know that the exponential growth equation is given by :-

$y=Ab^x$     (1)

, where A = initial amount.

b = Multiplicative rate of change.

x= Time period.

Given : Ms. Walker starts the fund by depositing $5.

⇒ A = $5

Each week the balance of the fund is twice the balance of the previous week.

⇒ b= 2

For x= number of weeks, substitute the value of A and b in (1), we get

$y=5(2)^x$  

The equation to the number of weeks, x, after which the balance of the fund will reach $1,280 will be :-

$1280=5(2)^x$   [Put y= 1280]

$\Rightarrow\ (2)^x=\dfrac{1280}{5}=256$

$\Rightarrow\ 2^x=2^8$              [∵ $2^8=256$]

$\Rightarrow\ x=8$   [∵ is $a^m=a^n \Rightarrow m=n$]

Hence, it will take 8 weeks to reach the class goal.

Answer 2

What you can use for this case is a function of the potential type.
 We have then
 y = a (b) ^ x
 Where we have:
 Walker starts the fund by depositing $ 5
 a = 5
 Each week the balance of the fund is twice the balance of the previous week:
 b = 2
 The function is:
 y = 5 (2) ^ x
 The number of weeks to reach $ 1280 is 8 weeks.
 Check:
 y = 5 (2) ^ 8
 y = 1280
 Answer:
 An equation can be used to find the number of weeks, x, after which the balance of the fund will reach $ 1,280 is:
 y = 5 (2) ^ x
 The number of weeks that it takes to reach the class goal is
 8 weeks