Video Transcript
The number of marine organisms in a
pool, 𝑦, after 𝑛 weeks is given by the formula 𝑦 equals 5,631 multiplied by a
half to the power of 𝑛 minus one. How many marine organisms will
there be in the pool after four weeks? Give your answer to the nearest
whole number.
This is an example of an
exponential growth model, as the variable representing time — in this case 𝑛, which
represents the number of weeks — is part of the exponent.
We’re asked to determine how many
marine organisms will be in the pool after four weeks, which means we’re looking to
determine the value of 𝑦 when 𝑛 is equal to four. To do so, we substitute 𝑛 equals
four into the exponential growth model for 𝑦, giving 𝑦 equals 5,631 multiplied by
a half to the power of four minus one. That’s 5,631 multiplied by a half
cubed, or 5,631 multiplied by one-eighth. We can evaluate this on a
calculator, and it gives 703.875.
Returning to the question though,
we were asked to give our answer to the nearest whole number. So as the first decimal place is an
eight, we need to round our answer up to 704. Using the given exponential growth
model then, we can conclude that after four weeks there will be 704 organisms living
in the pool to the nearest whole number.
