a = 252, x = 7; y = 5925.13
Equation is given by the formula:
[tex]y\text{ = y}_0\cdot(1+r)^{^x}{}[/tex]
where:
yo = the initial population; r = growth rate, x = time
In your case, yo = 252. And the grow rate is 57%, therefore the r = 0.57. Finally, the exponential equation has this form:
[tex]y\text{ = 252}\cdot1.57^x[/tex]
Then, if we want to know what is the population after 7 days, we can evaluate this function:
[tex]y\text{ \lparen7\rparen = 252}\cdot1.57^7\text{ =5925.13}[/tex]
