The amount, in dollars, of Marisa’s savings account, can be represented by the expression 5x + 40. Marisa saved the same amount x each month for a period of 5 months. Her mother contributed an additional amount each month to Marisa’s savings account. How much did her mother contribute each month?
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Answer:
To solve this, we can create an equation for the value based on time. So if we let t be the nmbers of years that have passed, we can create a function f(t) for the value in the savings account.
We note that f(0) =5000. (We invest 5000 at time 0.) Next year, he will have 5% more than that. To find our total value at the end of the year, we multiply 5,000 * 1.05 = 5,250. f(1) = 5000(1.05)=5,250. At the end of year 2, we will have a 5% growth rate. In other words, f(2) = (1.05)* f(1). We can rewrite this as f(2)=5000(1.05)(1.05)=5000(1.05)2 . We can begin to see the proper equation is f(t)=5000(1.05)t. If we plug in t = 15, we will have our account balance at the end of 15 years. So, our answer is f(15)=5000(1.05)15=10,394.64.
Step-by-step explanation:
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