Question

The population of Dwarf cats doubles in a certain country every year, as shown in the graph. If the number of Dwarfs cats was $ 50 $ last year, calculate the number of Dwarf cats after $ 4 $ years from now?
$ \left( a \right){\text{ 200}} $
$ \left( b \right){\text{ 250}} $
$ \left( c \right){\text{ 800}} $
$ \left( c \right){\text{ 1600}} $

Answer 1

Hint: This question can be done by observing the graph and by using the geometric progression concept. From the given figure we can see that the relationship is exponential and which is at the time $ t = 0 $ and by using G.P we will solve the problem.

Complete step-by-step answer:
First of all we will see the data given to us. As we can see from the graph, it is in exponential nature and also it is given that
The number of Dwarfs cats is $ 50 $ .
Since it is given that the numbers are getting doubled each passing year and from this, we will have the dwarf cat which at any given time is following a G.P series and from this, we will have the common ratio of $ 2 $ .
So, at any time $ t $ , let us assume the number of dwarf cats be $ y $
Therefore, by using the concept of G.P, the number of dwarfs cat will be $ y = 50\left( {{2^t}} \right) $
Since, we have to calculate it after the $ 4 $ years, so by substituting the values of time we get
 $ \Rightarrow y = 50\left( {{2^4}} \right) $
Now on solving the power inside the braces, we get
 $ \Rightarrow y = 50\left( {16} \right) $
And on solving the multiplication of the above equation, we get
 $ \Rightarrow 800 $
Therefore, the number of Dwarf cat after $ 4 $ years from now will be $ 800 $
So, the correct answer is “Option C”.

Note: This type of question is based on a certain concept and for this, we have to be familiar with the formulas and concepts we are going to use. Here, we had used the G.P concept and the formula of G.P will be given by $ {T_n} = a{r^{n - 1}} $ here, $ r $ will be the common ratios.