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An exponential function can either represent growth or decay
- The initial value is 200 and the growth factor is 1.190
- The number of fish in the pond after 5 years is 436
<u>(a) The initial number of fish and the growth factor</u>
The function is given as:
An exponential function is represented as:
Where
- a represents the initial value
- b represents the growth factor
So, by comparison: the initial value is 200
The growth factor is then calculated as:
Hence, the initial value is 200 and the growth factor is 1.190
<u>(b) The number of fish after 5 years</u>
This means that t = 5.
So, we have:
Hence, the number of fish in the pond after 5 years is 436
Read more about exponential functions at:
ABC is not a right angled triangle
<em><u>Solution:</u></em>
Given that, Triangle ABC has perimeter 18 cm
AB = 7 cm
BC = 3 cm
We have to find whether ABC is a right angled triangle
Let the sides of triangle be AB, BC, AC
<em><u>Perimeter of triangle is given by formula:</u></em>
perimeter = sum of length of all three sides of triangle
18 = AB + BC + AC
18 = 7 + 3 + AC
AC = 18 - 10
AC = 8
Thus the length of sides of triangle are:
AB = 7 cm
BC = 3 cm
AC = 8 cm
For a triangle to be right angle, it must satisfy the pythagoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
The longest side of triangle is hypotenuse
Therefore, AC = 8 cm is the hypotenuse
Thus by above theorem we get,
Substituting the values we get,
Thus the pythagoras theorem is not satisfied
Thus ABC is not a right angled triangle