Question

possible points 20
the area covered by a lake is 11 square kilometers. it is decreasing exponentially at a rate of 2 percent each year and can be modeled by $a(t) = 11 \cdot (.98)^t$.
which expression models the area of the lake after one decade?
a $\frac{11 \cdot (.98)}{10}$
b $11 \cdot (.98)^1$
c $11 \cdot (10)^{11}$
d $11 \cdot (.98)^{10}$

Explanation:

Step1: Identify time value

One decade = 10 years, so $t=10$.

Step2: Substitute t into the model

Replace $t$ with 10 in $A(t)=11\cdot(.98)^t$.
<Expression>
$A(10)=11\cdot(.98)^{10}$
</Expression>

Answer:

D. $11 \cdot (.98)^{10}$