This is a paragraph. You can put text in it. Or a list...
Text can be used with metadata (above). Put things like $avg will give random number between 5 and 17, rounded to two decimal places.
Questions hold one or several queries.
This is a fill-in-the-odUUwJR8n9a9EShm query. This is a ioSyxwBaqAfwJg7DU4J1p9B7JjBJc90snBvbXJCst6c= query.
AIMf15PROwh/unW6/Xr/RG1c93jhYd3VaAd7BKV5zJrY4RdHovieGWOqiEmg/BqlJ2/+gqP0qWTTbGiPUlbSIjFt4MnDBdpVVSE/zY+lPS+oZ9rKnXDuP4N/h4pubcPcn/YuyNSQiV7xaqpD0meMo2kr2YcVJA938YFd1FZtyKsjD6hf/1ZzutpaGWURGkxqQSE2H9apJQ/TuRWtPFs4kOYvvxBcuKTeXmA61lRMDWx487jZ/WDZUtlXvd5Q9UHo09rV8hSgmEdhpSLDCEAnbvlFY9TDSqitsKqD/53EEJwERMXMPvFSzEkD8gzw6kzqWs7LK4UbJLQZtrAPhlgSMfsvjSkygPHrU3h2JXPA8fZwafT2This is a new paragraph to be added after the Test question.
The content of the box.
This is a fill-in-the-odUUwJR8n9a9EShm query. It only appears if it is enclosed in a QUESTION. It doesn't requier METADATA, but will set some defaults. METADATA defined above may be used here.
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This is cell number FB:*1 | Cell 2 |
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Cell 0VV1JcqyBrI= | Cell 2 |
UThjyvT6D5k8Ejv3msuGWNTrHBEqbDRXIzeQZfwr9R8= | cell4 |
The rate of change of f(t) is the ratio of the change in f(t) divided by the unit change in t.
The account balance f(t) is measured in JvMTWtHHPxcVgRd4iHmpHpAOkxQe6GvTNzwj4lqqJTw= and t is measured in EFBAAtjIr6f0KWQKxGhjyzhRKP+ZNnARzqfy/+h/RGY=.
The average rate of change of y = f(t) over the interval [t0, t1] is given by the following.
Average rate of change =
Find the average rate of change over the interval [0, 0.5]. (Round your answers to two decimal places.)
For the interval [0.0, 0.5], let t0= 0 and t1 = ot+qaZUmHUo=.
In this case, f(t1) = 100*(iSba6t70dtA=
Thus the average rate of change is ogclm5qspRNIZA6hUagrKN0l3ew=.
Find the average rate of change over the interval [0, 1]. (Round your answers to two decimal places.)
For the interval [0, 1], let t0= 0 and t1 = 0VV1JcqyBrI=.
In this case, f(t1) = 100*(FB:*$b)1 and f(t0) = 100*(FB:*$b)0
Thus the average rate of change is FB:*$avgroc00to10.
Recall that the instantaneous rate of change at t = t0 is the limit of the average rates of change.
To estimate the instantaneous rate of change of the given problem, we calculate the average rate of change over smaller and smaller intervals to the nO/+DAdRVq+2oOvmzNgeN0ocEUKz3yEuOTAqpssC58Q= of t = ot+qaZUmHUo=
First calculate the average rate of change over three intervals to the right of t = 0.5. (Round your answers to four decimal places.)
Interval | [0.5, 0.51] | [0.5, 0.501] | [0.5, 0.5001] |
---|---|---|---|
Average rate of change | KM4Y0fTBDKXkN24kA9uYBg== | tOpUvmG3/QKqNS+t06QXwA== | BM6dDvGjjeFBDTN8BeDEVg== |
This table suggests the limit of the average rates of change as t approaches 0.5 from the left is approximately XFnw9W4YV2DY62VqrYm0C8FUhMM= dollars per year (rounded to two decimal places).
Now calculate the average rate of change over three intervals to the left of t = 0.5. (Round your answers to four decimal places.)
Interval | [0.49, 0.5] | [0.499, 0.500] | [0.4999, 0.5000] |
---|---|---|---|
Average rate of change | bECI2HMu3zb8FISFiyvzAg== | AqHQgaV4SHbsguD1jWG/hg== | HZJ3TiwmXftPFf5AM9MwDw== |
This table suggests the limit of the average rates of change as t approaches 0.5 from the left is approximately FB:*$avg499999toH dollars per year (rounded to two decimal places).
Based on the previous questions, the instantaneous rate of change at t = 0.5 is approximately L1roKTQ32O/N3Yl8O0Zde3nASJA= dollars per year (rounded to two decimal places).