We are given function E(t) = 4^8*4^t to approximates the number of nematodes in a certain sample of fresh compost,
t is the time in number of days.
We need to find the initial number of nematodes.
We need to take t=0 for find the initial number of nematodes, because initial number of minutes will be 0.
So, we just need to plug t=0 in the given function.
a) Plugging t=0 in given function
E(t) = 4^8*4^t, we get
E(0) = 4^8 * 4^0.
Please note: Power 0 of any number or term always have a value 1.
Therefore, 4^0 = 1.
Plugging this value in above equation.
E(0) = 4^8 * 4^0 = 4^8 *1
E(0) = 4^8.
Therefore, 4^8 number of nematodes are there initially.
b) In second part, we need to find the number of nematodes after 3.5 days.
Plugging t=3.5 in given function, we get
E(3.5) = 4^8 * 4^(3.5).
4^(3.5) = 128 and 4^8= 65536
Therefore,
E(3.5) = 4^8 * 4^(3.5) = 65536 * 128 = 8388608.
Therefore, 8,388,608 nematodes are there after 3.5 days.
And Option B. 4^8; 8,388,608 is correct option.