Question

Question 1 (1 point)

In a lab, 370 cells are present at the beginning of an experiment. During the first 9 hours, the number of cells increased by 10% each hour.
Write an exponential model giving the number of cells y present thours after starting the experiment. Estimate the time when the number of
cells is 600.
o
a
c
y = 370(1.1)
; after about 5 hours
y = 370(0.1)", after about 10 hours
y = (370. 1.1) after about 1 hour
= 370(0.9)
; after about 0.5 hour
C
1



plssss I need this now ​

Answer 1

Model: y = 370 * (1.1)^t

Time for 600 cells: after about 5 hours

Explanation:

The function that models an exponencial growth is:

y = Po * (1 + r)^t

Where y is the final value, Po is the inicial value, r is the rate and t is the time.

In this case, we have that Po = 370 and r = 10% = 0.1, so our model is:

y = 370 * 1.1^t

To find the time when the number of cells will be 600, we just need to use y = 600 and then calculate for t:

600 = 370 * 1.1^t

1.1^t = 600/370

1.1^t = 1.6216

log(1.1^t) = log(1.6216)

t * log(1.1) = log(1.6216)

t * 0.0953 = 0.4834

t = 0.4834 / 0.0953 = 5.0724 hours