Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%
compounded monthly. After 14 years, how much more money would Damian have in
his account than Sophie, to the nearest dollar?

Step-by-step explanation:

The formula we need for each of these calculations is

which is the formula for interest that compounds continuously. We will first figure the amount that Sophie has after that 14 years, then we will figure out the amount that Damian has after 14 years, and then find the difference. Sophie's interest as a decimal is .06125; Damian's is .06625.

and

and

and

Sophie has $216,867.94 after 14 years.

Now for Damian's account:

and

and

and

Damian has $232,592.64 after 14 years.

Damian has 232592.64 - 216867.94 more than Sophie, which is $15,724.70

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week