Question

Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours. Match the following statements to their interpretations, given below. (a) f(7) = 2.9 : ? (b) f^-1(7) = 12 : ? (c) f'(7) = 0.1 : ? (d) (f^-1)'(7) = 4 : ? Interpretations: 1: at 7 AM, 2.9 centimeters of rain have fallen 2: when 4 centimeters have fallen, rain is accumulating at a rate of 1/7 hr/cm, so it takes approximately 8.6 min for the total accumulation to go from 4 to 5 cm 3: at 2.9 hours past midnight, 7 centimeters of rain have fallen 4: 7 centimeters of rain have fallen 12 hours after midnight 5: at 7 hours after midnight, 0.1 centimeters of rain have fallen 6: at 4 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 1.17 cm of rain falls between 4 AM and 4:10 AM 7: at 7 AM, the rain is falling at a rate of 0.1 cm/hr, so approximately 0.0017 cm of rain falls between 7 AM and 7:01 AM 8: 0.1 centimeters of rain have fallen 7 hours after midnight 9: when 4 centimeters of rain have fallen, rain is falling at a rate of 7 cm/hr, so it takes approximately 8.6 min for the total accumulation to go from 4 to 5 cm 10: when 7 centimeters of rain have fallen, it is accumulating at a rate of 1/4 hr/cm, so it takes approximately 24 min for the total accumulation to go from 7 to 7.1 cm 11: at 7 hours after midnight, 12 centimeters of rain have fallen 12: at 0.1 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 0.58 cm of rain falls in the next five minutes 13: at 12 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 0.1167 cm of rain falls in the next minute 14: when 4 centimeters have fallen, rain is accumulating at a rate of 1/7 hr/cm, so it takes approximately 42 min for the total accumulation to go from 4 to 4.1 cm 15: at 7 hours after midnight, rain is falling at a rate of 4 cm/hr, so approximately 0.67 cm of rain falls in the next ten minutes 16: at 7 AM, rain is falling at a rate of 2.9 cm/hr, so approximately 0.24 cm of rain falls in the next five minutes

          Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours. Match the following statements to their interpretations, given below.
(a) f(7) = 2.9 : ?
(b) f^-1(7) = 12 : ?
(c) f'(7) = 0.1 : ?
(d) (f^-1)'(7) = 4 : ?

Interpretations:
1: at 7 AM, 2.9 centimeters of rain have fallen
2: when 4 centimeters have fallen, rain is accumulating at a rate of 1/7 hr/cm, so it takes approximately 8.6 min for the total accumulation to go from 4 to 5 cm
3: at 2.9 hours past midnight, 7 centimeters of rain have fallen
4: 7 centimeters of rain have fallen 12 hours after midnight
5: at 7 hours after midnight, 0.1 centimeters of rain have fallen
6: at 4 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 1.17 cm of rain falls between 4 AM and 4:10 AM
7: at 7 AM, the rain is falling at a rate of 0.1 cm/hr, so approximately 0.0017 cm of rain falls between 7 AM and 7:01 AM
8: 0.1 centimeters of rain have fallen 7 hours after midnight
9: when 4 centimeters of rain have fallen, rain is falling at a rate of 7 cm/hr, so it takes approximately 8.6 min for the total accumulation to go from 4 to 5 cm
10: when 7 centimeters of rain have fallen, it is accumulating at a rate of 1/4 hr/cm, so it takes approximately 24 min for the total accumulation to go from 7 to 7.1 cm
11: at 7 hours after midnight, 12 centimeters of rain have fallen
12: at 0.1 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 0.58 cm of rain falls in the next five minutes
13: at 12 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 0.1167 cm of rain falls in the next minute
14: when 4 centimeters have fallen, rain is accumulating at a rate of 1/7 hr/cm, so it takes approximately 42 min for the total accumulation to go from 4 to 4.1 cm
15: at 7 hours after midnight, rain is falling at a rate of 4 cm/hr, so approximately 0.67 cm of rain falls in the next ten minutes
16: at 7 AM, rain is falling at a rate of 2.9 cm/hr, so approximately 0.24 cm of rain falls in the next five minutes

Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours. Match the following statements to their interpretations, given below.
(a) f(7) = 2.9 : ?
(b) f^-1(7) = 12 : ?
(c) f'(7) = 0.1 : ?
(d) (f^-1)'(7) = 4 : ?

Interpretations:
1: at 7 AM, 2.9 centimeters of rain have fallen
2: when 4 centimeters have fallen, rain is accumulating at a rate of 1/7 hr/cm, so it takes approximately 8.6 min for the total accumulation to go from 4 to 5 cm
3: at 2.9 hours past midnight, 7 centimeters of rain have fallen
4: 7 centimeters of rain have fallen 12 hours after midnight
5: at 7 hours after midnight, 0.1 centimeters of rain have fallen
6: at 4 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 1.17 cm of rain falls between 4 AM and 4:10 AM
7: at 7 AM, the rain is falling at a rate of 0.1 cm/hr, so approximately 0.0017 cm of rain falls between 7 AM and 7:01 AM
8: 0.1 centimeters of rain have fallen 7 hours after midnight
9: when 4 centimeters of rain have fallen, rain is falling at a rate of 7 cm/hr, so it takes approximately 8.6 min for the total accumulation to go from 4 to 5 cm
10: when 7 centimeters of rain have fallen, it is accumulating at a rate of 1/4 hr/cm, so it takes approximately 24 min for the total accumulation to go from 7 to 7.1 cm
11: at 7 hours after midnight, 12 centimeters of rain have fallen
12: at 0.1 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 0.58 cm of rain falls in the next five minutes
13: at 12 hours after midnight, rain is falling at a rate of 7 cm/hr, so approximately 0.1167 cm of rain falls in the next minute
14: when 4 centimeters have fallen, rain is accumulating at a rate of 1/7 hr/cm, so it takes approximately 42 min for the total accumulation to go from 4 to 4.1 cm
15: at 7 hours after midnight, rain is falling at a rate of 4 cm/hr, so approximately 0.67 cm of rain falls in the next ten minutes
16: at 7 AM, rain is falling at a rate of 2.9 cm/hr, so approximately 0.24 cm of rain falls in the next five minutes

Added by Heather P.

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