To begin a bacteria study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 15%.Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.Write an exponential function showing the relationship between y and t.

Accepted Solution

Answer:The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]Step-by-step explanation:Given[tex]t[/tex] be the number of hours.[tex]y[/tex] number of bacteria cells.And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponentThe petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]In the equation as [tex]C[/tex] is function of  time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]Check:[tex]15\% of 1800 =0.15\times 1800=270[/tex]So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]That can also be from the formula.[tex]C(t)=1800(1.15)^1=2070[/tex]So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex][tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.