Question

the expression $6.7 \cdot 1.45^t$ models the number of billions of genetic sequence bases available in the public database of the whole genome shotgun project $t$ years since 2002.
what does $1.45$ represent in this expression?
choose 1 answer:
a the number of bases in the database is multiplied by $1.45$ each year.
b it is $1.45$ years since 2002
c there were $1.45$ billion bases in the database in 2002.

Explanation:

The expression \(6.7 \cdot 1.45^t\) is an exponential growth model. In exponential growth \(y = a \cdot b^t\), \(b\) represents the growth factor (the factor by which the quantity is multiplied each time period). Here, \(t\) is years since 2002, so \(1.45\) is the factor the number of bases is multiplied by each year. Option B is wrong because \(t\) represents years since 2002, not \(1.45\). Option C is wrong because the initial amount (when \(t = 0\)) is \(6.7\) (since \(1.45^0=1\)), so the initial number of bases in 2002 is \(6.7\) billion, not \(1.45\).

Answer:

A. The number of bases in the database is multiplied by 1.45 each year.