Marcus was giving dollar bills from his grandfather each day for one week. on the first day he received one dollar, on the second day he received two dollars, on the third day he received four dollars, and on the fourth day he received eight dollars. if this pattern continues, how much money will marcus have by the end of the week

Marcus will make $127 by the end of the month.

Step-by-step explanation:

On the first day he received one dollar, on the second day he received two dollars, on the third day he received four dollars, and on the fourth day he received eight dollars. This means that the amount of money he receives is increasing in a geometric progression.

The sum of n terms of a sequence is expressed as

Sn = a(r^n - 1)/(r - 1)

Where

a is the first term of the sequence

r is the common ratio,

n is the number of terms.

From the information given,

n = 7( a week is 7 days)

a = 1 (amount for the first day)

r = 2

S7 = 1(2^7 - 1)/(2-1)

S7 = 128 - 1 = 127

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.