(b) express using functional - notation the circulation of the magazine 18 months after it was…

(b) express using functional - notation the circulation of the magazine 18 months after it was started.\nc(15)\nfind that value. (round your answer to two decimal places.)\n5.02 (thousand magazines)\n(c) over what time interval is the graph of c concave up?\nthe graph of c is concave up from t = 0 (smaller value) to t=\nexplain what \concave up\ means in practical terms.\nthe circulation was increasing more and more slowly.\nthe circulation was increasing more and more quickly.\nthe circulation was decreasing more and more slowly.\nthe circulation was decreasing more and more quickly.\n(d) at what time was the circulation increasing the fastest? (round your answer to the nearest integer.)\nt = 0 years\n(e) determine the limiting value for c.\nc=\nexplain your answer in practical terms.

(b) express using functional - notation the circulation of the magazine 18 months after it was started.\nc(15)\nfind that value. (round your answer to two decimal places.)\n5.02 (thousand magazines)\n(c) over what time interval is the graph of c concave up?\nthe graph of c is concave up from t = 0 (smaller value) to t=\nexplain what \concave up\ means in practical terms.\nthe circulation was increasing more and more slowly.\nthe circulation was increasing more and more quickly.\nthe circulation was decreasing more and more slowly.\nthe circulation was decreasing more and more quickly.\n(d) at what time was the circulation increasing the fastest? (round your answer to the nearest integer.)\nt = 0 years\n(e) determine the limiting value for c.\nc=\nexplain your answer in practical terms.

Answer

Explanation:

Step1: Analyze functional - notation for 18 months

Since time $t$ is in years and 18 months = 1.5 years, the functional notation is $C(1.5)$.

Step2: Analyze concavity

A function $y = C(t)$ is concave - up when its second - derivative $C''(t)>0$. In practical terms, when a function is concave up, the rate of change of the function is increasing. For the circulation function $C(t)$, this means the circulation was increasing more and more quickly.

Step3: Find the time when circulation is increasing fastest

The circulation is increasing fastest at the inflection point (where the concavity changes). Without the actual function or more detailed graph information, we assume based on the concept of concavity. If the function is concave up first and then changes, the point where the concavity changes is where the slope of the tangent line is the steepest in the increasing part.

Step4: Determine the limiting value

Without the actual function or more information about the long - term behavior of the circulation function $C(t)$, we cannot determine the limiting value accurately. But conceptually, it could be the maximum value the circulation approaches as $t$ gets very large.

Answer:

(b) $C(1.5)$ (c) The graph of $C$ is concave up from $t = 0$ to some value (not given precisely in the problem). Concave up means the circulation was increasing more and more quickly. (d) Cannot be determined precisely without more information about the function or the graph. (e) Cannot be determined precisely without more information about the long - term behavior of the function.