The number of e. coli bacteria cells in a pond of stagnant water can be represented by the function below, where a represents the number of e. coli bacteria cells per 100 ml of water and t represents the time, in years, that has elapsed.

a(t)=136(1.123)^4t

based on the model, by approximately what percent does the number of e. coli bacteria cells increase each year?

a.

60%

b.

59%

c.

41%

d.

40%

Explanation:

The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:

The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:

Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.

addition

step-by-step explanation:

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%