Population Attributes

In the population growth curves shown below, ‘a’ and ‘b’ is representing:

The spread of a disease can be modelled by the equation $y=4+e^x$, where $x$ is the time in days. Find the number of days it takes for $25000$ people to be affected.

(Use: $\ln 24996=10.13$)

The spread of a disease can be modelled by the equation $y=4+e^x$, where $x$ is the time in days. Find the number of people with the disease after seven days.

The temperature, $T^{°}C$, of a cup of soup can be modelled by the equation $T\left(x\right)=21+74\times (1.2{)}^{-x}$ where $x$ is the time in minutes. Find the temperature after $10$ minutes.(Give the answer correct upto two decimal places.)

The temperature, $T^{°}C$, of a cup of soup can be modelled by the equation $T\left(x\right)=21+74\times (1.2{)}^{-x}$ where $x$ is the time in minutes. Find the initial temperature in degree Celsius.

The population of rabbits can be modelled by the function $f\left(x\right)=24000\times 1.{12}^x$, where $x$ is the time in years. Find the number of rabbits after five years. 

A funny joke is spreading through the office. The speed that it is spreading can be modelled by the equation $f\left(x\right)=4+e^x$, where $x$ is the time in minutes and $x\ge 0$. Find how many minutes it took before $150$ employees heard the joke.(Give the answer correct up to two decimal place)(Use: $\ln 146=4.98$)

A funny joke is spreading through the office. The speed that it is spreading can be modelled by the equation $f\left(x\right)=4+e^x$, where $x$ is the time in minutes and $x\ge 0$. Find out many employees heard the joke initially.

The spread of a virus can be modelled by the equation $f\left(x\right)={10}^x$, where $x$ is the time in weeks.Find how many people have the virus after two weeks.

The length of a pumpkin plant, in metres, can be modelled by the equation $f\left(x\right)=e^x$, where $x$ is the time in weeks after the pumpkin is planted. Find the number of weeks it takes for the plant to reach $10$ metres.(Give the answer correct upto one decimal place)

The length of a pumpkin plant, in metres, can be modelled by the equation $f\left(x\right)=e^x$, where $x$ is the time in weeks after the pumpkin is planted. Find the initial length of the pumpkin plant.

The temperature, $T°\mathrm{C},$ of a cup of hot chocolate can be modelled by the equation $T\left(x\right)=70(1.45{)}^{-x}+21$, where $x$ is the time in minutes. Find the number of minutes it takes for the hot chocolate to reach $50°\mathrm{C}$. (Use $\log 0.4142=-0.3828$, $\log 1.45=0.1614$ and give the answer correct up to two decimal places)

The temperature, $T°\mathrm{C},$ of a cup of hot chocolate can be modelled by the equation $T\left(x\right)=70(1.45{)}^{-x}+21$, where $x$ is the time in minutes. Find the temperature after five minutes in degree Celsius (correct upto one decimal place).

The temperature, $T°\mathrm{C},$ of a cup of hot chocolate can be modelled by the equation $T\left(x\right)=70(1.45{)}^{-x}+21$, where $x$ is the time in minutes. Find the initial temperature of the hot chocolate in degree Celsius.

A radioactive material has been spilled on farmland and the quantity remaining can be modelled by the equation $f\left(x\right)=130(0.85{)}^x,$ where $x$ is the time in years and $f\left(x\right)$ is the mass in grams. Calculate how many years it takes before only half the material remains (round off the answer upto one decimal place).

A radioactive material has been spilled on farmland and the quantity remaining can be modelled by the equation $f\left(x\right)=130(0.85{)}^x,$ where $x$ is the time in years and $f\left(x\right)$ is the mass in grams. Find the mass after four years (round it off to $1$ decimal place). 

A radioactive material has been spilled on farmland and the quantity remaining can be modelled by the equation $f\left(x\right)=130(0.85{)}^x,$ where $x$ is the time in years and $f\left(x\right)$ is the mass in grams. Find the initial mass of the material in grams.