Question

Two weeks before an examination day, a librarian monitored the number of students who visited the library. Then they compared it with the number of visits made in an average week. Approximately 2×103 visits were reflected in their logbook during this two-week period, while only about 5×102 were reflected on an average week. How many times higher is the number of library visits before examination day compared to the library visits in an average week? Your answer should be a whole number.

Answer 1

It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a×10n where a is single digit.

Answer 2

To find the number of times higher the number of library visits before the examination day is compared to an average week, we need to compare the number of visits in the two-week period to the number of visits in one average week.

The number of visits in the two-week period is 2 × 10^3.

The number of visits in one average week is 5 × 10^2.

To find the number of times higher, we divide the number of visits in the two-week period by the number of visits in one average week:

(2 × 10^3) / (5 × 10^2) = (2/5) × (10^3/10^2) = (2/5) × 10^1 = 0.4 × 10 = 4

Therefore, the number of library visits before the examination day is 4 times higher than the number of visits in an average week.

Answer 3

To find the value of "n" for the expression a×10n, we can use the formula:

P = A / (1 + r)^n

Where:
P = initial deposit ($100)
A = final amount ($15,528.23)
r = interest rate per period (5% or 0.05)
n = number of periods (months or years)

Since the interest is compounded monthly, we need to convert the 10-year period into months:

n = 10 years * 12 months/year = 120 months

Substituting the given values into the formula:

100 = 15,528.23 / (1 + 0.05)^120

Now we solve for (1 + 0.05)^120:

(1.05)^120 ≈ 4.3219

So, 4.3219 * 100 ≈ 432.19

Therefore, the value of "a" is approximately 4, and the value of "n" is 2.

Thus, $15,528.23 can be expressed as 4.32x10².