Answer:
Step-by-step explanation:
In the exponential growth/decay function
, in our situation,
y is the number of ants remaining in the colony after the growth or decay,
a is the initial number of ants in the colony, and
b is the growth/decay rate. Rule: if b is greater than 1, the function is growth; if b is greater than 0 but less than 1, the function is decay.
Our equation looks like this (it's given):
a = 50, which is the initial number of ants in the colony.
b = .8 (which actually means that then number of ants is declining by 20% each week). Since .8 is a fraction of 1, this is decay.
So far, we know that 1 and 4 are true. Let's look at 5. We have to do some solving to find out if it's true or not. If the number of ants after x = 2 weeks is 32, then we plug in 2 for x and see if the y we get as the answer is 32:
and
y = 50(.64) so
y = 32
5 is true as well. Let's test 6 by replacing x with 8 and seeing if y = 10:
and
y = 50(.16777216) so
y = 8.388
6 is not true.
1, 4, 5 are true