The city library started with 1,000 books, and the number of books grows continuously at a rate of 3% per year. Create an exponential expression to model the number of books the library will have after t years. Then, match each part of the exponential expression to what it represents in the context of the situation.
The proportion of growth
is 0.03 or 3%.
The percentage multiplied
by the number of years
years is 0.03t.
is the number of books
multiplied by e.
The initial number
of books is 1,000.
The growth speed is
.
This is continuous growth
which is represented by
.
Base:
Coefficient:
Rate:
Exponent:
Base: e
Coefficient: 1,000
Rate: 0.03 or 3%
Exponent: t
Exponential expression: 1000e^(0.03t)
Part representations:
Base: The number of books is multiplied by e.
Coefficient: The initial number of books is 1,000.
Rate: The proportion of growth is 0.03 or 3%. This is continuous growth which is represented by e.
Exponent: The percentage multiplied by the number of years (t) is 0.03t.