Answer:
b = 9.1units
Step-by-step explanation:
Find the diagram attached
Using the similarity theorem of triangle
WX/XZ = WY/WX
Substitute;
b/a+5 = 6/b
b² = 6(a+5) ... 1
Also according to pythagoras theorem on triangle WYX;
b² = 6²+a²...2
Equate 1 and 2
6(a+5) = 6²+a²
6a+30 = 36 + a²
a²-6a+36-30 = 0
a²-6a+6 = 0
a = 6±√36+4(6)/2
a = 6±√60/2
a = 6±7.745/2
a = 13.745/2
a = 6.8725
Recall that
b² = 6²+a²
b² = 36+6.8725²
b² = 83.2313
b = 9.12units
b = 9.1units
Given exponential function
f(x)=
Where x is the number of years
f(x) is the number of tuna in thousands
To find out when number of tuna is 50 thousand , we plug in 50 for f(x) and solve for x
Divide by 230 on both sides
Take ln on both sides
Divide by ln(0.881) on both sides
x =
x= 12.04
Year = 1974 + 12.04 = 1986
so in 1986 there will be 50 thousand tuna.