The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and \( t \) is the time in years, express \( N \) as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using \( t \) as the variable and in terms of \( e \).) (b) If the population doubled in size over 14 months and the current population is 60,000 , what will the population be 4 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

If \( f(x)=\sqrt{x+4} \) and \( g(x)=\frac{5}{x} \), then which of the following does \( (f \circ g)(x) \) equal? Choose the correct answer below. \( \frac{5}{\sqrt{x}}+4 \) \( \frac{\sqrt{\frac{5}{x+4}}}{\frac{5}{\sqrt{x+4}}} \) \( \sqrt{\frac{5}{x}+4} \)

Find the domain of the function. \[ g(x)=\ln (x-7) \] The domain of \( g \) is (Type your answer in interval notation.)

¿Cómo se define el factor de crecimiento en una función exponencial?

Which transformations must be applied to obtain the graph of \( f(x)=5^{x+4} \) ? Select all that apply. \( \square \) A. Horizontal compression or stretch \( \square \) B. Reflection about the \( y \)-axis \( \square \) C. Reflection about the \( x \)-axis \( \square \) D. Vertictal shift \( \square \) E. Vertical compression or stretch \( \square \) F. Horizontal shift

Let \( f(x)=\frac{3 x^{2}+4 x+1}{4 x^{2}+14 x-8} \) This function has: 1) Ay intercept at the point 2) \( x \) intercepts at the point(s) 3) Vertical asymptotes of vertical asymptote first) 4) Horizontal asymptote of