Rochelle deposits $6,000 in an IRA. What will be the value (in dollars) of her investment in 15 years if the investment is earning 9% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)

$ 23,145

Step-by-step explanation:

This is a compound interest question where the interest is compounded continuously. Hence, the formula for the value of total amount of investment is:

A = P×e^rt

Where:

A = Total value of investment after t years

P = Principal or Initial amount invested = $6,000

e = Exponential function

r = interest rate = 9% = 0.09

t = time in years = 15

So:

A = $6000 × e^15 × 0.09

A = $6000 × e^1.35

A = $23,144.553184

Approximately , A ≈$23,145

Therefore, the value (in dollars) to the nearest cent of Rochelle's investment in 15 years if the investment is earning 9% per year and is compounded continuously is $23,145.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.