Answer
$
P(t)=3.1(1.25)^t
$
$
P(t)=1.3+0.04 t
$
Work Step by Step
A) World cocoa production:
To see if the data can be modelled as a linear or exponential function, we test the differences an the ratios of the successive data values.Since $3.875-3.1=0.775$ and $4.844-3.875=0.969$, the data is no linear. Next,
$$
\frac{3.875}{3.1}=1.25, \quad \frac{4.844}{3.875}=1.250, \quad \frac{6.055}{4.844}=1.25, \quad \frac{7.568}{6.055}=1.250
$$
Clearly, the data can be modelled as an exponential function. The base is $b= 1.25$ and $a= 3.1$ The world cocacola production can be modelled as
$$
P(t)=3.1(1.25)^t
$$
B) Ivory coast cocoa production:
$$
1.34-1.3=0.04, \quad 1.38-1.34=0.04
$$
The data can be modelled as linear function. The slope is $m= 0.04$ and vertical intercept is $b= 1.3$ The Ivory Coast cocacola production can be modelled as
$$
P(t)=1.3+0.04 t
$$
