A fast growing mushroom doubled in size every day. After 30 days, it measured 6 inches tall. On which day did it measure 1 1/2 inches tall?
size = a(2)^t , where t is the number of days
when t = 30 , size = 6
6 = a(2)^30
a = 6/2^30
1.5 = ( 6/(2^30) )( 2^t)
1.5 = 6 (2^(t-30) )
.25 = 2^(t-30)
log .25 = log 2^(t-30)
log .25 = (t-30)log 2
log .25/log 2 = t-30
t = log .25/log 2 + 30 = appr 23.356
23 days and 8.5 hours
Hmmm. It doubles every day.
6 = 4 * 1 1/2, so it must have taken the last 2 days to double twice from 1 1/2 to 3 to 6 inches.
I say it took 28 days.
I'd have stopped at
.25 = 2^(t-30)
-2 = t-30
t = 28
Not sure what went wrong after that.
To find the day on which the mushroom measured 1 1/2 inches tall, we can work backward from the information given.
First, we will determine the growth rate of the mushroom by dividing its final size (6 inches) by the number of days it took to reach that size (30 days).
Growth rate = Final size / Number of days
Growth rate = 6 inches / 30 days
Growth rate = 0.2 inches per day
Since the mushroom doubles in size every day, we can divide the current size by 2 to find the size on the previous day.
On the first day, the mushroom measured:
Current size = 1.5 inches
Previous day's size = Current size / 2
Previous day's size = 1.5 inches / 2
Previous day's size = 0.75 inches
To determine the number of days it took for the mushroom to reach 0.75 inches, we can divide the previous day's size by the growth rate.
Number of days = Previous day's size / Growth rate
Number of days = 0.75 inches / 0.2 inches per day
Number of days ≈ 3.75 days
Based on this calculation, it took approximately 3.75 days for the mushroom to grow from 0.75 inches to 1.5 inches tall. Therefore, the mushroom measured 1 1/2 inches tall on the 4th day.
To solve this problem, we can use the concept of exponential growth since the mushroom doubles in size every day. Let's start by finding out the size of the mushroom on day 1.
Day 1: 1/2 inch (half the size of 1 inch)
Now, let's see the growth of the mushroom over time:
Day 2: 1 inch (doubled in size)
Day 3: 2 inches (doubled in size again)
...
Day 29: 3 inches
Day 30: 6 inches
From the given information, we know that on day 30 the mushroom measured 6 inches tall. We want to find out on which day it measured 1 1/2 inches tall.
To do this, we can work backward and halve the size until we reach 1 1/2 inches:
Day 29: 3 inches (halved in size)
Day 28: 1.5 inches (halved in size again)
So, the mushroom measured 1 1/2 inches tall on day 28.