E Exponential and Logarithmic Functions Writing an equation that models exponential growth or decay To begin a bacteria study, a petri dish had 2000 bacteria cells. Each hour since, the number of cells has increased by \( 17 \% \). Sydney Write an exponential function showing the relationship between \( y \) and \( t \).

To model the bacterial growth, we can use the exponential growth formula: \( y = y_0(1 + r)^t \), where \( y_0 \) is the initial amount, \( r \) is the growth rate, and \( t \) is the time in hours. Here, the initial number of bacteria \( y_0 \) is 2000, and the growth rate \( r \) is 0.17 (since 17% as a decimal is 0.17). Therefore, the equation will be: \[ y = 2000(1 + 0.17)^t \] or simplified: \[ y = 2000(1.17)^t \] In practical terms, if you want to monitor the bacteria's growth, this equation allows you to predict the population at any hour by simply plugging in the value of \( t \). For instance, if you want to know how many bacteria there will be after 5 hours, you substitute \( t = 5 \) into the equation. Math becomes a cool tool in the lab!