A principle of $2400 is invested at 7.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? Write the smallest possible whole number answer.

Step-by-step explanation:To find the interest accumulated over a period of time you use:

A = P [1 + (r/n)]^(nt)

with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.

A = 2000

P = 1500

r = 0.035

n=1

Thus you get:

2000 = 1500 (1+0.035)^t

Divide by 1500:

(4/3) = (1.035)^t

Apply "ln" on both sides:

ln(4/3) = t*ln(1.035)

Calculate the logarithms:

0.28768 = t*0.03440

Divide by 0.03440 on both sides:

t = 8.36 years

So after approximately 8 years and 5 month you will have $2000 or more in the account.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

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step-by-step explanation: