Answer:
4%
Step-by-step explanation:
A = final amount
P = initial amount
r = interest rate per time period
n = number of times compounded per time period
t = number of time period
A = 3932.82
r = what we want to find
n = 2
t = 6
divide both sides by 3101 to isolate the exponent and its parts
put both sides to the power of (1/12) to help isolate the variable
subtract 1 from both sides to isolate the variable and its coefficient
multiply both sides by 2 to get r
r ≈ 0.04 = 4%
Part A
The sequence is geometric because the y values are doubling each time
4*2 = 8
8*2 = 16
16*2 = 32
The common ratio is r = 2.
<h3>Answer: Geometric</h3>=======================================================
Part B
The recursive rule here would be
The first line says that "the first term is 4"
The second line says "the nth term is found by multiplying 2 by the previous (n-1) term". In other words, double any term to get the next term.
The fourth term is 32 which doubles to 64 and that's the fifth term. So the point (5,64) is on this exponential curve.
Answer: She takes <u>64 minutes</u> to complete station 5
========================================================
Part C
We see that a = 4 is the first term and r = 2 is the common ratio.
The explicit nth term formula is a(r)^(n-1) which becomes 4(2)^(n-1)
Plugging in the value n = 8 leads to
4(2)^(n-1)
4(2)^(8-1)
4(2)^7
4(128)
512
You can use the method shown in part B to keep doubling each term until you arrive at the 8th term. This is one way to confirm the answer.
<h3>Answer: 512 minutes</h3>