In 2020 , there 58 alligators in New Town, Florida. The number of alligators increased by $15 \%$ per year afterwards. Assume that conditions are favorable and that alligator population growth can be modeled exponentially as $f(x)=a(1+r)^{z}$ where $=$ - initial population, $r=g r o w t h$ rate, and $x=$ number of years. How many alligators will there be in New Town, Florida in 2030? Round you answer to the nearest whole number (no partial alligators please!).
Final Answer: There will be approximately \(\boxed{235}\) alligators in New Town, Florida in 2030.
Step 1 :Given that in 2020, there were 58 alligators in New Town, Florida. The number of alligators increased by 15% per year afterwards. We are asked to find the number of alligators in 2030.
Step 2 :We can model the alligator population growth exponentially as \(f(x)=a(1+r)^{x}\) where \(a\) is the initial population, \(r\) is the growth rate, and \(x\) is the number of years.
Step 3 :Substitute the given values into the formula: \(a=58\), \(r=0.15\), and \(x=2030-2020=10\).
Step 4 :Calculate the result: \(f(x)=58(1+0.15)^{10}\).
Step 5 :The result is approximately 234.64234867105858.
Step 6 :Round the result to the nearest whole number, as we cannot have partial alligators.
Step 7 :Final Answer: There will be approximately \(\boxed{235}\) alligators in New Town, Florida in 2030.