Jacob deposits $60 into an investment account with an interest rate of 4%, compounded annually. The equation,
y = 60(1 + 0.04)x, can be used to determine the number of years, x, it takes for Jacob's balance to reach a certain amount of money, y. Jacob graphs the relationship between time and money.
What is the y-intercept of Jacob's graph?
If Jacob doesn't deposit any additional money into the account, how much money will he have in eight years? Round your answer to the nearest cent.
Hi There!
I will be glad to help you with this problem.
I will get you started.
y = 60(1 + 0.04)^x = 60 * 1.04^x
At the y-intercept, x = 0:
y = 60 * 1.04^0
y = 60 * 1
y = 60
Then,
y = 60 * 1.04^8
y = 60 * 1.3685690504052736
(Please multiply that part!)
y = ????
Hint:
The y-intercept of Jacob's graph is...
In eight years Jacob will have...
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Please feel free to post your response and someone may probably check it.
y = 60(1 + 0.04)^x = 60 * 1.04^x
At the y-intercept, x = 0:
y = 60 * 1.04^0
y = 60 * 1
y = 60
Therefore the y-intercept is 60.
In order to see how much he'll have in his account after 8 years you must substitute 8 into the equation.
y = 60 * 1.04^8
y = 60 * 1.3685690504052736
y = 82.11 (rounded to the nearest hundredth)
Jacob will have $82.11 in his investment account after 8 years.
If I'm being honest I'm mostly just guessing but you can check if you want.
Why did the scarecrow go into the investment business? Because he heard it was a great way to grow his straw-tune!
Now, let's get to Jacob's graph!
The y-intercept of Jacob's graph represents the initial amount of money he deposited into the investment account. In this case, the y-intercept is $60.
If Jacob doesn't deposit any additional money into the account and the interest is compounded annually, we can use the equation y = 60(1 + 0.04)^x to find out how much money he will have in eight years. Plugging in x = 8, we get:
y = 60(1 + 0.04)^8
y = 60(1.04)^8
Calculating that, we find y ≈ $79.29.
So, without any additional deposits, Jacob will have approximately $79.29 in eight years. That's quite a straw-mazing growth!
To find the y-intercept of Jacob's graph, we need to determine the value of y when x is equal to zero.
Substituting x = 0 into the equation y = 60(1 + 0.04)x, we get:
y = 60(1 + 0.04)0
y = 60(1)
y = 60
Therefore, the y-intercept of Jacob's graph is 60.
If Jacob doesn't deposit any additional money into the account, we can calculate the balance after 8 years using the compound interest formula.
Substituting x = 8 into the equation y = 60(1 + 0.04)x, we get:
y = 60(1 + 0.04)8
y = 60(1.04)8
y = 60(1.3605)
y ≈ 81.63
So, Jacob will have approximately $81.63 in eight years.
To find the y-intercept of Jacob's graph, we need to determine the value of y when x is equal to zero. This represents the initial amount of money in Jacob's account.
Plugging in x = 0 into the equation y = 60(1 + 0.04)x, we get:
y = 60(1 + 0.04)^0
y = 60(1)
y = 60
Therefore, the y-intercept of Jacob's graph is 60. This means that when Jacob initially deposited $60 into the investment account, his balance started at $60.
To find out how much money Jacob will have in eight years, we substitute x = 8 into the equation y = 60(1 + 0.04)x. Let's calculate it:
y = 60(1 + 0.04)^8
y ≈ 60(1.04)^8
y ≈ 60(1.36049) [Rounding to the nearest cent]
y ≈ $81.63
After eight years, Jacob will have approximately $81.63 in his account if he doesn't deposit any additional money.