colony contains 1500 bacteria. The population increases at a rate of $$ 115 \% $$ each hour. If $$ x $$ represents the number hours elapsed, which function represents the scenario? $$ f(x)=1500(1.15)^{x} $$ $$ f(x)=1500(115)^{x} $$ $$ f(x)=1500(2.15)^{x} $$ $$ f(x)=1500(215)^{x} $$

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To model the growth of the bacteria colony, we need to use an exponential growth function of the form:

$$ f(x) = f_0 \cdot (1 + r)^x $$

Where:
- $$ f_0 $$ is the initial population.
- $$ r $$ is the growth rate per time period.
- $$ x $$ is the number of time periods elapsed.

**Given:**
- Initial population ($$ f_0 $$) = 1500 bacteria
- Growth rate ($$ r $$) = 115% per hour = 1.15 in decimal form
- Time ($$ x $$) = number of hours

However, **interpreting "increases at a rate of 115%"** means that each hour, the population increases by **115% of the current population**, resulting in a new population that is:

$$ \text{New Population} = \text{Current Population} + 1.15 \times \text{Current Population} = 2.15 \times \text{Current Population} $$

Thus, the exponential growth function becomes:

$$ f(x) = 1500 \cdot (2.15)^x $$

**Answer:**
$$ f(x) = 1500 \times (2.15)^{\,x} $$

**Selected Option:**
$$ f(x)=1500(2.15)^{x} $$
The function representing the scenario is $$ f(x) = 1500(2.15)^{x} $$.

colony contains 1500 bacteria. The population increases at a rate of \( 115 \% \) each hour. If \( x \) represents the number hours elapsed, which function represents the scenario? \( f(x)=1500(1.15)^{x} \) \( f(x)=1500(115)^{x} \) \( f(x)=1500(2.15)^{x} \) \( f(x)=1500(215)^{x} \)

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