Answer :
To determine the multiplicative rate of change for the function [tex]\( f(x) = 2 \cdot 5^x \)[/tex], we need to understand how the function changes as [tex]\( x \)[/tex] increases.
1. Identify the form of the function:
The function given is [tex]\( f(x) = 2 \cdot 5^x \)[/tex], where [tex]\( 2 \)[/tex] is a constant and [tex]\( 5^x \)[/tex] is an exponential term with base [tex]\( 5 \)[/tex].
2. Understand multiplicative rate of change:
In an exponential function of the form [tex]\( a \cdot b^x \)[/tex], the multiplicative rate of change is determined by the base [tex]\( b \)[/tex]. This base [tex]\( b \)[/tex] indicates how much the function is multiplied by when [tex]\( x \)[/tex] increases by 1.
3. Analyze the function:
For the function [tex]\( f(x) = 2 \cdot 5^x \)[/tex]:
- When [tex]\( x \)[/tex] increases by 1, the function is multiplied by the base of the exponent, which is [tex]\( 5 \)[/tex].
4. Conclusion:
Therefore, the multiplicative rate of change of the function [tex]\( f(x) = 2 \cdot 5^x \)[/tex] is [tex]\( 5 \)[/tex].
Based on this analysis, the correct answer is:
[tex]\[ \boxed{5} \][/tex]
1. Identify the form of the function:
The function given is [tex]\( f(x) = 2 \cdot 5^x \)[/tex], where [tex]\( 2 \)[/tex] is a constant and [tex]\( 5^x \)[/tex] is an exponential term with base [tex]\( 5 \)[/tex].
2. Understand multiplicative rate of change:
In an exponential function of the form [tex]\( a \cdot b^x \)[/tex], the multiplicative rate of change is determined by the base [tex]\( b \)[/tex]. This base [tex]\( b \)[/tex] indicates how much the function is multiplied by when [tex]\( x \)[/tex] increases by 1.
3. Analyze the function:
For the function [tex]\( f(x) = 2 \cdot 5^x \)[/tex]:
- When [tex]\( x \)[/tex] increases by 1, the function is multiplied by the base of the exponent, which is [tex]\( 5 \)[/tex].
4. Conclusion:
Therefore, the multiplicative rate of change of the function [tex]\( f(x) = 2 \cdot 5^x \)[/tex] is [tex]\( 5 \)[/tex].
Based on this analysis, the correct answer is:
[tex]\[ \boxed{5} \][/tex]
