Algebra 2 (picture shown)

M(13)=14.3 gram

Step-by-step explanation:

Exponential Decay Function

The exponential function is used to model natural decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The element has an initial mass of Mo=970 grams, the decaying rate is r=27.7% = 0.277 per minute.

The equation of the model is:

Operating:

After t=13 minutes the remaining mass is:

Calculating:

M(13)=14.3 gram

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;