Answer:
Rate[tex]\rightarrow[/tex] the proportion of growth is 0.03 or 3%
Co-efficient [tex]\rightarrow[/tex] The initial number of books is 1000
Exponent[tex] \rightarrow[/tex] The percentage multiplied by number of years is [tex]0.03t[/tex]
base[tex]\rightarrow[/tex] This is continuous growth which is represented by [tex]e[/tex]
Step-by-step explanation:
Given:
Initial number of books = 1000
Rate of growth = 3%
To find the exponential expression to model the number of books in the library after [tex]t[/tex] years.
Solution:
The continuous exponential growth equation is given by:
[tex]F_v=P_ve^{rt}[/tex]
where [tex]F_v\rightarrow[/tex] final value
[tex]P_v\rightarrow[/tex] initial value
[tex]e\rightarrow[/tex] exponential [tex]e=2.71828183....[/tex]
[tex]r\rightarrow[/tex] rate of growth
[tex]t\rightarrow[/tex] time
Given data:
[tex]P_v=1000\ books\\r=3\%=0.03\\t=t \ years[/tex]
Plugging in the given values in the formula:
[tex]F_v=1000e^{0.03t}[/tex]
So, we have
Rate[tex]\rightarrow[/tex] the proportion of growth is 0.03 or 3%
Co-efficient [tex]\rightarrow[/tex] The initial number of books is 1000
Exponent[tex] \rightarrow[/tex] The percentage multiplied by number of years is [tex]0.03t[/tex]
base[tex]\rightarrow[/tex] This is continuous growth which is represented by [tex]e[/tex]
