The scientist prepared an inoculation medium by adding $2.4\times 10^{-4}g$ of dried Chlorella cells to $1{dm}^3$ of sterile nutrient solution. The average dry mass of a single microalga cell is $2.4\times 10^{-11}g$. Calculate the initial number of algal cells in this inoculation medium. Give your answer in standard form.

Under optimal light and nutrient conditions, the population of this microalga doubles every $30minutes$. Using an initial culture containing $1.0\times 10^7$ cells, the scientist plots the log-transformed population size, ${\log }_{10}(number\; of\; cells)$, against time $t$ (in hours) over the first $15hours$.

Determine:

• The coordinates of the starting point of the growth curve at $t=0h$.
• The coordinates of the ending point of the growth curve at $t=15h$, using the standard approximation $2^{10}\approx 10^3$.
• A description of the shape of the growth curve under these optimal conditions.