One less than the product of four and a number is 11. What is that number ?
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Answer:
12%
Step-by-step explanation:
The equation for the growth is ...
f(t) = (initial value)×(growth multiplier per period)^(number of periods)
where the growth multiplier is often expressed as a percentage added to 1:
multiplier = 1+r
growth rate = r
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This equation has two unknowns:
- initial value
- growth multiplier
In order to find these, you can make use of two of the supplied data points. I like to choose the ones that are farthest apart, as they tend to average out any errors due to rounding.
Clearly, the table tells you the initial value is 210. If you don't believe, you can put the numbers in the equation to see that:
f(0) = (initial value)×(growth multiplier)^0
210 = (initial value)×1
(initial value) = 210
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Using the last data point, we get ...
f(7) = 210×(growth multiplier)^7
464 = 210×(growth multiplier)^7 . . . . . . . . . fill in table value
2.209524 = (growth multiplier)^7 . . . . . . . divide by 210
You can solve this a couple of ways. My calculator is able to take the 7th root, so I can use it to find ...
Alternatively, you can use the 1/7 power:
2.209524^(1/7) = (growth multiplier)
Another way to solve this is to use logarithms:
log(2.209524) = 7×log(growth multiplier) . . . . . take the log
log(2.209524)/7 = log(growth multiplier) . . . . . divide by 7
0.04918553 ≈ log(growth multiplier)
growth multiplier = 10^0.04918553 ≈ 1.11992 . . . . take the antilog
So, our growth multiplier is ...
1 + r ≈ 1.11992
r ≈ .11992 ≈ 12.0%
The rate of growth is about 12% in each period.
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Collapsing all of that to a single calculation:
growth rate = (464/210)^(1/(7-0)) -1 ≈ 12.0%
The value of b in the exponential function which is formed by Shanna for the price of land is 8% or 0.08.
<h3>What is percentage increase ?</h3>Percentage increase is the amount added to the initial value in the percentage part.
The value of a plot of land which is increases 8% every year has the current value of $350000.
The final value owner wants is $570000. Shanna writes an exponential function of the form, to model the value,v, of the land in t years as,
Here, in this exponential function the value of a is fixed or initial term which is $350000 and the value of b is the constant term which is change factor. Here, the value of b is 8%.
b=8%
b=8/100
b=0.08
Thus, the value of b in the exponential function which is formed by Shanna for the price of land is 8% or 0.08.
Learn more about the percentage increase here;
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