Question

You deposit $400 into a savings account that earns interest annually. The function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[0, 400]
[0, ∞)
[400, ∞)

Answer 1

Answer:

Step-by-step explanation:

The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.  

With an example, what is compound interest?

When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits.

Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.

Principal - $400

rate of interest is compounded annually

g(x) =  400( 1.03)ˣ equation 1.

Formula used

A = P( 1 + r )ⁿ

here n = x

Solution:

Putting the value of n, and principal in the formula

A = P( 1 + r )ⁿ ................... equation 2

now comparing both equation 1 and equation 2,

400( 1.05)ˣ =  400( 1 + r )ˣ

( 1.05)ˣ = ( 1 + r  )ˣ

1.05 = 1 + r

r = 1.05 - 1

r = 0.05

r % = 0.05 × 100

r % = 5 %

thus, the constant percent rate of change =  5 %

Learn more about compound interest

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