which of the following equations represents exponential growth? (select all that apply)\n□ $f(x) = -2x…

which of the following equations represents exponential growth? (select all that apply)\n□ $f(x) = -2x - 5$\n□ $h(t) = 4(1.2)^{3x - 2}$\n□ $f(x) = 3x^2 + 2x - 4$\n□ $g(x) = 3(-5)^x$\n□ $p(t) = 300(1.05)^t$

which of the following equations represents exponential growth? (select all that apply)\n□ $f(x) = -2x - 5$\n□ $h(t) = 4(1.2)^{3x - 2}$\n□ $f(x) = 3x^2 + 2x - 4$\n□ $g(x) = 3(-5)^x$\n□ $p(t) = 300(1.05)^t$

Answer

Brief Explanations:

To determine exponential growth, we use the form ( y = ab^x ) where ( a>0 ) and ( b > 1 ) (for growth; if ( 0 < b < 1 ), it's decay). Let's analyze each function:

  1. ( f(x)=-2x - 5 ): This is linear (degree 1), not exponential.
  2. ( h(t)=4(1.2)^{3x - 2} ): Rewrite as ( 4(1.2)^{-2}(1.2)^{3x} ). Here, ( a = 4(1.2)^{-2}>0 ) and ( b=(1.2)^3>1 ) (since ( 1.2 > 1 )), so it represents exponential growth.
  3. ( f(x)=3x^2 + 2x - 4 ): This is quadratic (degree 2), not exponential.
  4. ( g(x)=3(-5)^x ): The base ( -5 ) is negative, so it's not a valid exponential growth/decay function (exponential functions require ( b>0, b\neq1 )).
  5. ( P(t)=300(1.05)^t ): Here, ( a = 300>0 ) and ( b = 1.05>1 ), so it represents exponential growth.

Answer:

( h(t) = 4(1.2)^{3x - 2} ), ( P(t) = 300(1.05)^t )