1. **State the problem:** We are given an exponential function modeling bacteria population growth: $$f(x) = 575(1 + 0.40)^x$$ where $x$ is time in hours and $f(x)$ is population in thousands. 2. **Identify the parameters:** The function is of the form $$f(x) = a b^x$$ where: - $a = 575$ represents the initial population (at $x=0$). - $b = 1 + 0.40 = 1.40$ represents the growth factor per hour. 3. **Interpret $a$:** Since $a = 575$, the initial population is $$575 \times 1000 = 575,000$$ bacteria. 4. **Interpret $b$:** The growth factor $b = 1.40$ means the population increases by 40% each hour. 5. **Calculate the growth rate as a percentage:** The growth rate is $$(b - 1) \times 100 = (1.40 - 1) \times 100 = 40\%$$ per hour. 6. **Check the statement about 140% growth:** The statement "population is increasing at a rate of 140% per hour" is incorrect because 140% growth would mean $b = 2.40$ (since $1 + 1.40 = 2.40$). 7. **Summary:** - Initial population: 575,000 bacteria. - Growth rate: 40% per hour. **Final answer:** The initial population was 575,000 bacteria, and the population increases by 40% each hour, not 140%.