Chapter 7.6, Problem 42PPE

To determine

To analyse: The presence of more than 5000 hydra.

Answer to Problem 42PPE

  $y=60\left(2^x\right)$

Explanation of Solution

Given information:

Hydra is small freshwater animals. They can double in number every twodays in a laboratory tank with an initial population of 60 hydra.

Formula used:

  $y=a{b}^x$

Calculation:

The initial population of Hydra is 60 and they become double for every two days

Consider the table

  

Hence, it is observed that after 14 days the population of Hydra more than 5000.

Suppose that no of days represented by the variable x and the population of Hydra representedby the variable y .Then from the table it is clear that there is a constant difference between xvalues and there is a constant ratio between the y values. So the above table represents anexponential function. The Hydra grows exponentially.

In an exponential function $y=a{b}^x,\text{'}a\text{'}$ represents the initial number and ‘b' represents thecommon ratio. From the table $a=60\text{and }b=2$ . So the exponential function models the situation is $y=60\left(2^x\right)$

Conclusion:

The exponential function models the situation is $y=60\left(2^x\right)$