Answer:
look search math-way and type your problem in .
Step-by-step explanation:
Answer:
The population of bacteria is increasing.
Step-by-step explanation:
The function modelling the population of bacteria in the given culture is an exponential function; We have a base 1.03 and an exponent t. An exponential function is said to be increasing if the base is strictly greater than 1, this implies that the population of the bacteria is increasing as t increases from 0 to infinity.
Yes. Parallel means same slope as original line. So it’s 2
Answer:
The function for the outside temperature is represented by
, where t is measured in hours.
Step-by-step explanation:
Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:
Amplitude
![A = \frac{100\º-70\º}{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B100%5C%C2%BA-70%5C%C2%BA%7D%7B2%7D)
![A = 15\º](https://tex.z-dn.net/?f=A%20%3D%2015%5C%C2%BA)
Mean temperature
![\bar T = \frac{70\º+100\º}{2}](https://tex.z-dn.net/?f=%5Cbar%20T%20%3D%20%5Cfrac%7B70%5C%C2%BA%2B100%5C%C2%BA%7D%7B2%7D)
![\bar T = 85\º](https://tex.z-dn.net/?f=%5Cbar%20T%20%3D%2085%5C%C2%BA)
Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:
![T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right]](https://tex.z-dn.net/?f=T%28t%29%20%3D%20%5Cbar%20T%20%2B%20A%20%5Ccdot%20%5Csin%20%5Cleft%5B2%5Cpi%5Ccdot%5Cfrac%7Bt-6%5C%2Ch%7D%7B%5Ctau%7D%20%5Cright%5D)
Where:
- Mean temperature, measured in degrees.
- Amplitude, measured in degrees.
- Daily period, measured in hours.
- Time, measured in hours. (where t = 0 corresponds with 5 AM).
If
,
and
, the resulting function for the outside temperature is:
![T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]](https://tex.z-dn.net/?f=T%28t%29%20%3D%2085%5C%C2%BA%20%2B%2015%5C%C2%BA%20%5Ccdot%20%5Csin%20%5Cleft%5B%5Cfrac%7Bt-6%5C%2Ch%7D%7B24%5C%2Ch%7D%20%5Cright%5D)
Answer:
x = -5
Step-by-step explanation:
Get x by itself on the left side. To do that, subtract the 7. Do to both sides. This makes x = -5