Answer:
Given,
The initial population, P = 87,000,
Annual rate of increasing, r = 1.9 %,
a) Thus, the population after t years,
Where, k is the rate constant,
By comparing,
Hence, the approximate value of k is 0.00817.
And, the exponential growth function would be,
b) If A = 145,000,
By using graphing calculator,
We get,
The year after 27 years from 2016 is 2043.
Hence, in 2043 the population reach 145,000.
A=P (1+r/n)^nt
A= Total amount invested, P=principal amount, r=Interest rate, n=number of time in a year when the interest is earned (for annual, n=1; for semi-annual, n=2, ...), t = time in years
In the current scenario, case 1, n=2; case 2, n=1 and A1=A2, t1=t2
Therefore,
800(1+0.0698/2)^2t = 1000(1+0.0543/1)t
Dividing by 800 on both sides;
(1+0.0349)^2t = 1.25(1+0.02715)^t
(1.0349)^2t = 1.25(1.02715)^t
Taking ln on both sides of the above equation;
2t*ln (1.0349)= ln 1.25 + t*ln (1.02715)
2t*0.0343 = 0.2231+ t*0.0268
0.0686 t = 0.2231+0.0268 t
(0.0686-0.0268)t = 0.2231
0.0418t=0.2231
t=5.337 years
Therefore, after 5.337 years or 5 years and approximately 4 months, their value of investments will be equal.
This value will be,
A=800(1+0.0698/2)^2*5.337 = $1,153.76
Answer:
5/3 or 1.666...
Step-by-step explanation:
SLOPE: get the difference of each coordinate and divide them.
two points: A(2,7) and B(5,12)
we subtract ax from bx:
5 - 2 = 3, "dx"
and subtract ay from by:
12 - 7 = 5, "dy"
now we divide dy/dx:
5/3 or 1.666...
that's the slope
Answer:
steps below
Step-by-step explanation:
1. 1 + 1/2*(n-1) : 3, 7/2, 4, 9/2
2. 1 + 1/3*(n-1): 7/3, 8/3, 9/3, 10/3
3. 3/2 + 1/2*(n-1): 4, 9/2, 5
4. 1, 4, 16, 19, 76...79, 316, 319, 1276 ...
